Answer:
Yes, they form a partition
Step-by-step explanation:
For a group of sets to be considered a partition of set A (currently enrolled students), all of the elements in set A must be contained in the subsets that form the partition and no individual element can be present in more than one subset.
In this situation, take set A0 for instance, all students whose ID numbers begin with 0 will be in this set and in this set alone. The same can be said for Ai where i ∈ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. Since no other possible value can be assigned for the first digit of an student ID, it is correct to affirm that sets A0, …, A9 form a partition of the set of currently enrolled students.
Final answer:
The sets A0, A1, ..., A9, where each set consists of students whose ID starts with a specific digit, form a partition of the set of all currently enrolled students because each set is non-empty, the sets are mutually exclusive, and their union represents the entire set of students.
Explanation:
To understand if the sets A0, A1, ..., A9, form a partition of the set of currently enrolled university students based on their 8-digit ID numbers starting with digits 0 through 9, three conditions must be met: each set must be non-empty, the sets must be mutually exclusive, and their union must form the entire set of currently enrolled students.
Non-empty Sets: Given that for each digit i, there is at least one student whose ID starts with i, all sets A0 through A9 meet the criterion of being non-empty.Mutually Exclusive: Since each student is assigned a unique 8-digit ID, and an ID can only start with one digit, the sets are mutually exclusive; a student whose ID starts with a 1, for example, cannot also be in the set of IDs beginning with 2.Union Forms the Entire Set: Because all possible ID numbers will begin with a digit from 0 to 9, the union of sets A0 through A9 covers every currently enrolled student making them a partition of the set of all students.Thus, the sets A0 through A9 form a partition of the set of all currently enrolled students.
To estimate LaTeX: \muμ, the mean salary of full professors at American colleges and universities, you obtain the salaries of a random sample of 400 full professors. The sample mean is LaTeX: \bar{x} = $73,220 x ¯ = $ 73 , 220 and the sample standard deviation is s = $4400. A 99% confidence interval for LaTeX: \mu μ is Group of answer choices
A. 73220 +/- 11440
B. 73220 +/- 568
C. 73220 +/- 431
D. 73220 +/- 28.6
Answer:
99% confidence interval for [tex]\mu = 73220 \pm 565.4[/tex]
Step-by-step explanation:
Sample mean = [tex]\bar{x} =73220[/tex]
Standard deviation = s = 4400
Z at 99% confidence level = 2.57
Sample = n = 400
Formula of confidence interval :[tex]\bar{x} \pm Z \times \frac{s}{\sqrt{n}}[/tex]
Substitute the values in the formula :
So,99% confidence interval for [tex]\mu = 73220 \pm 2.57 (\frac{4400}{\sqrt{400}})[/tex]
99% confidence interval for [tex]\mu = 73220 \pm 565.4[/tex]
What is the answer to the problem?
Answer:
a
Step-by-step explanation:
good luck :)
Poornima is a stay-at-home parent who lives in San Francisco and teaches tennis lessons for extra cash. At a wage of $30 per hour, she is willing to teach 3 hours per week. At $50 per hour, she is willing to teach 7 hours per week. Using the midpoint method, the elasticity of Poornima's labor supply between the wages of $30 and $50 per hour is approximately(1.6,0.13,0.63,25) , which means that Poornima's supply of labor over this wage range is (elastic, inelastic)
Answer:
We can deduce that the elasticity of the labor supply is greater than 1 the labor supply is considered elastic
Step-by-step explanation:
The formula to use is the following:
Elasticity = (Change in working hours / Average working hours) / (Change in wage rate / Average wage rate)
we replace the data
Elasticity = [(7 - 3) / (7 + 3) / 2] / [(50 - 30) / (50 + 30) / 2]
Elasticity = [4 / (10/2)] / [20 / (80/2)]
Elasticity = (4/5) / (20/40)
Elasticity = 0.8 / 0.5
OUTCOME
Elasticity = 1.6
We can deduce that the elasticity of the labor supply is greater than 1 the labor supply is considered elastic
The elasticity of Poornima's labor supply between the wages of $30 and $50 per hour is approximately 1.5. This shows that Poornima's supply of labor in this wage range is elastic, indicating responsiveness to wage changes.
Explanation:The elasticity of labor supply can be calculated using the midpoint method. This method measures elasticity as the percent change in quantity supplied divided by the percent change in wage. The percent change in quantity supplied is calculated as (Q2-Q1)/[(Q1+Q2)/2], where Q1 = 3 and Q2 = 7. That gives us (7-3)/[(3+7)/2] = 1. The percent change in wage is calculated similarly as (P2-P1)/[(P1+P2)/2], where P1 = $30 and P2 = $50, giving us (50-30)/[(30+50)/2] = 0.67. By dividing the percent change in quantity supplied by the percent change in wage, we get the elasticity of labor supply: 1/0.67 = 1.5 (rounded).
Therefore, the elasticity of Poornima's labor supply between wages of $30 and $50 per hour is approximately 1.5. Because the elasticity is greater than 1, Poornima's supply of labor over this wage range is elastic, meaning she is responsive to wage changes.
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A restaurant sells four combo meals. Jolly Meal, which cost $7, consists of 2 yogurt cups and 1 sandwich. The Special Meal, which is made up of 2 sandwiches and 1 yogurt cup, cost $12.50. Calculate the cost of the following combo meals if the charge for sandwiches and yogurt cups are the same for all combo meals.
Answer:
Yogurt: $0.50 Sandwich: $6
Step-by-step explanation:
Because if you make the combos equations it would be Y+Y+X=7 and X+X+Y=12.5 so you would solve with those and for it to work with both, 0.50 for yogurt, and 6 for sand which would work.
The volume of a cone is 565.2 cubic inches. The height of the cone is 15 inches. What is the radius of the cone, rounded to the nearest inch? (Use π = 3.14.) (1 point)
Group of answer choices
3
6
18
36
Answer:
Radius, r = 6 inches
Step-by-step explanation:
We have,
Volume of a cone is 565.2 cubic inches
Height of the cone is 15 inches
It is required to find the radius of the cone. Volume of a cone is given by :
[tex]V=\dfrac{1}{3}\pi r^2 h[/tex]
r is radius of cone
[tex]r=\sqrt{\dfrac{3V}{\pi h}} \\\\r=\sqrt{\dfrac{3\times 565.2}{3.14\times 15}} \\\\r=6\ \text{inch}[/tex]
So, the radius of the cone is 6 inches. The correct option is (b).
A family plans to have three children. The wife and husband are trying to determine the probabilities of the different gender outcomes for the children.
The husband thinks that the probability that the first child is a girl is greater than the probability that the first child is a girl and the second child is a girl. The wife disagrees. She thinks that the two probabilities are equal.
The sample space of possible outcomes is listed below. B represents a boy, and G represents a girl.
Who is correct, the husband or the wife?
The husband is correct; the probability of the first child being a girl is higher than the probability of the first two being girls.
Let's list the sample space of possible outcomes for the genders of three children:
1. BBB (all boys)
2. BBG (two boys, one girl)
3. BGB (one boy, one girl, one boy)
4. BGG (one boy, two girls)
5. GBB (one girl, two boys)
6. GBG (two girls, one boy)
7. GGB (two girls, one boy)
8. GGG (all girls)
Now, let's examine the probabilities the husband and wife are discussing:
1. Husband's claim: Probability of the first child being a girl is greater than the probability of the first two children being girls.
Probability of the first child being a girl: [tex]\( \frac{4}{8} = \frac{1}{2} \)[/tex]
Probability of the first two children being girls: [tex]\( \frac{2}{8} = \frac{1}{4} \)[/tex]
The husband is correct.
2. Wife's claim: Probability of the first child being a girl is equal to the probability of the first two children being girls.
Both probabilities are [tex]\( \frac{1}{2} \)[/tex].
The wife is incorrect.
Therefore, the husband is correct in this scenario.
The cost, not including tax, of paper and pens
at the card store is $21.79. The tax is 9% of
the selling price. What is the total cost of the
pens and pencils including tax?
The circumference of the inner circle is 88 ft. The distance between the inner circle and the outer circle is 3 ft. By how many feet is the circumference of outer circle greater than the circumference of the inner circle? Use StartFraction 22 Over 7 EndFraction
for pi.
Final answer:
The circumference of the outer circle is approximately 18.86 feet greater than the circumference of the inner circle, which has a circumference of 88 feet.
Explanation:
The circumference (C) of a circle is calculated using the formula C = 2πr, where π is Pi and r is the radius of the circle. Given that the circumference of the inner circle is 88 ft and the distance between the inner and outer circle is 3 ft, we deduce that the radius of the outer circle is 3 ft greater than the radius of the inner circle. Using the given approximation of π as 22/7, we can find the new circumference.
First, let's find the radius of the inner circle. Rearrange the formula to r = C / (2π) and substitute π with 22/7:
r = 88 / ((2 × 22)/7) = 88 / (44/7) = 88 / (6.2857) ≈ 14 ft
Now, the radius of the outer circle is r + 3 ft, which equals 17 ft. The circumference of the outer circle is then:
C = 2πr = 2 × 22/7 × 17 = 2 × 22 × 17 / 7 = 34 × 22 / 7 = 748 / 7 ≈ 106.86 ft
To find by how many feet the circumference of the outer circle is greater than the inner circle, subtract the circumference of the inner circle from that of the outer circle:
106.86 ft - 88 ft = 18.86 ft
Therefore, the circumference of the outer circle is approximately 18.86 ft greater than the circumference of the inner circle.
12 more than 8.2 times a number n is
Answer:
12+ 8.2n
Step-by-step explanation:
12 more than 8.2 times a number n is:
First, 12 more indicates that whatever we get has to add 12 on since it is 12 more.
Second, 8.2 times a number is multiplication and that number is filled in by a variable (n).
Therefore, the equation is 8.2n + 12
If 15 bahs are equal to 24 rahs, and 9 rahs are equal in value to 15 yahs, how many bahs are equal in value to 1000 yahs?
Answer:
375
Step-by-step explanation:
b : r = 15 : 24
r : y = 9 : 15 = 3 : 5 = 24 : 40
Then ...
b : r : y = 15 : 24 : 40
The number of bahs equivalent to 1000 yahs is ...
bahs = (15/40)(1000) = 375
375 bahs are equal in value to 1000 yahs.
the quesiton is in the picture
Answer:
The three equivalent options are: [tex]\frac{1}{6}x+47[/tex], [tex]\frac{5}{3}x+35-\frac{3}{2}x+12[/tex], and [tex]5(\frac{1}{3} x+(5)(7)-(3)(\frac{1}{2}x)+(3)(4)[/tex]
Step-by-step explanation:
Expand [tex]5(\frac{1}{3}x+7)-3(\frac{1}{2}x-4)[/tex] to get [tex]\frac{5}{3}x+35-\frac{3}{2}x+12[/tex].
Simplifying this gets you [tex]\frac{1}{6}x+47[/tex].
Hundreds, tens, and ones
hat number represents the same amount as 3 hundreds + 4 tens +16 ones?
Answer:
356
Step-by-step explanation:
3 hundreds = 3 * 100 = 300
4 tens = 4 * 10 = 40
16 ones = 16 * 1 = 16
Combine the terms: 300 + 40 + 16 = 356
356 is your answer.
~
The operations manager of a manufacturer of television remote controls wants to determine which batteries last the longest in his product. He took a random sample of his remote controls and tested two brands of batteries. Here are the number of minutes of continuous use before the batteries failed for each brand. Is there statistical evidence of a difference in longevity between the two batteries?
Answer:
There is not enough evidence to support the claim that the longevity of the two brand of batteries differs.
Step-by-step explanation:
The question is incomplete:
The sample data for each battery is:
Battery 1: 106 111 109 105
Battery 2: 125 103 121 118
The mean and STD for the sample of battery 1 are:
[tex]M_1=\dfrac{1}{4}\sum_{i=1}^{4}(106+111+109+105)\\\\\\ M_1=\dfrac{431}{4}=107.75[/tex]
[tex]s_1=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{4}(x_i-M)^2}\\\\\\s_1=\sqrt{\dfrac{1}{3}\cdot [(106-(107.75))^2+(111-(107.75))^2+(109-(107.75))^2+(105-(107.75))^2]}\\\\\\ s_1=\sqrt{\dfrac{1}{3}\cdot [(3.06)+(10.56)+(1.56)+(7.56)]}\\\\\\ s_1=\sqrt{\dfrac{22.75}{3}}=\sqrt{7.58333333333333}\\\\\\s_1=2.754[/tex]
The mean and STD for the sample of battery 2 are:
[tex]M_2=\dfrac{1}{4}\sum_{i=1}^{4}(125+103+121+118)\\\\\\ M_2=\dfrac{467}{4}=116.75[/tex]
[tex]s_2=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{4}(x_i-M)^2}\\\\\\s_2=\sqrt{\dfrac{1}{3}\cdot [(125-(116.75))^2+(103-(116.75))^2+(121-(116.75))^2+(118-(116.75))^2]}\\\\\\ s_2=\sqrt{\dfrac{1}{3}\cdot [(68.06)+(189.06)+(18.06)+(1.56)]}\\\\\\ s_2=\sqrt{\dfrac{276.75}{3}}=\sqrt{92.25}\\\\\\s_2=9.605[/tex]
This is a hypothesis test for the difference between populations means.
The claim is that the longevity of the two brand of batteries differs.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0[/tex]
The significance level is α=0.05.
The sample 1, of size n1=4 has a mean of 107.75 and a standard deviation of 2.754.
The sample 2, of size n2=4 has a mean of 116.75 and a standard deviation of 9.605.
The difference between sample means is Md=-9.
[tex]M_d=M_1-M_2=107.75-116.75=-9[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2+\sigma_2^2}{n}}=\sqrt{\dfrac{2.754^2+9.605^2}{4}}\\\\\\s_{M_d}=\sqrt{\dfrac{99.841}{4}}=\sqrt{24.96}=4.996[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{-9-0}{4.996}=\dfrac{-9}{4.996}=-1.8014[/tex]
The degrees of freedom for this test are:
[tex]df=n_1+n_2-1=4+4-2=6[/tex]
This test is a two-tailed test, with 6 degrees of freedom and t=-1.8014, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=2\cdot P(t<-1.8014)=0.122[/tex]
As the P-value (0.122) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the longevity of the two brand of batteries differs.
A car that normally sells for $20,000 is on sale for $16,000. What percent of the original price of the car is the final price?
Answer:
80%
Step-by-step explanation:
20000. take out 3 zeros from both numbers and you get 20 and 16. 20 is 4 times 5 and 16 is 4 times 4 if 20 is 100% then 4 over 5 is 80%
Which of the following is not true in hypothesis testing? The smaller the p-value, the less evidence the data provide against the null hypothesis and in favor of the alternative hypothesis. The larger the p value, the less evidence the data provide against the null hypothesis and in favor of the alternative hypothesis. The smaller the p value, the more evidence the data provide against the null hypothesis and in favor of the alternative hypothesis. None of the above
Answer:
The larger the p value, the less evidence the data provide against the null hypothesis and in favour of the alternative hypothesis
Step-by-step explanation:
P Value is the probability of obtaining extreme observed results in a statistical hypothesis test, assuming that null hypothesis is correct.
High p value implies evidence in favour of null hypothesis, against alternate hypothesis.
Low p value implies evidence against null hypothesis, in favour of alternate hypothesis
So, larger p value, more evidence the data provides in favour of null hypothesis & against alternate hypothesis.The incorrect statement about hypothesis testing is that a smaller p-value indicates less evidence against the null hypothesis.
A small p-value actually provides strong evidence against the null hypothesis, prompting its rejection.
The p-value measures how unlikely the observed data is under the null hypothesis, but does not indicate the truth of the null hypothesis itself.
The statement in hypothesis testing that is not true is The smaller the p-value, the less evidence the data provides against the null hypothesis and in favor of the alternative hypothesis.
A small p-value indicates that the observed test statistic is very unlikely if the null hypothesis is true, which provides stronger evidence against the null hypothesis and in favor of the alternative hypothesis.
In fact, we generally use a significance level (commonly < 0.05) to determine if we should reject the null hypothesis. On the contrary, a larger p-value suggests less evidence against the null hypothesis, implying that we are less likely to reject it.
It's important to remember that the p-value is the probability of obtaining the observed data, or more extreme, given that the null hypothesis is true.
It does not, however, describe the probability that the null hypothesis itself is true, thus a small p-value means that the data is unlikely under the null hypothesis, leading to its potential rejection.
Pablo runs 7 miles in 80 minutes. At the same rate, how many miles would he run in 64 minutes?
Which graph represents a function with a rate of change of 0.5?
On a coordinate plane, a line with negative slope goes through points (negative 1, 1) and (0, negative 1).
On a coordinate plane, a line with negative slope goes through points (negative 2, 0) and (0, negative 1).
On a coordinate plane, a line with positive slope goes through points (0, negative 1) and (1, 1).
On a coordinate plane, a line with positive slope goes through points (0, negative 1) and (2, 0).
Answer: D-On a coordinate plane, a line with positive slope goes through points (0, negative 1) and (2, 0). plz mark me brainliest.
Step-by-step explanation:
Option D. is correct. On a coordinate plane, a line with positive slope goes through points (0, negative 1) and (2, 0).
Which graph represents a function with a rate of change of 0.5?
What are functions?Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is independent variable while Y is dependent variable.
since
given rate of change = 0.5
slope of curve = rate of change
slope = [tex]\frac{Y_2-Y_1}{X_2-X_1}[/tex]
we have (0,-1) and (2, 0)
slope = 0+1/2-0
= 1/5
=0.5
=rate of change
Thus, On a coordinate plane, a line with positive slope goes through points (0, negative 1) and (2, 0).
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Steph runs a vehicle body repair shop with one mechanic in Cleveland. Repair time for vehicles is exponentially distributed, with a mean of 2.8 minutes per vehicle. Customers arrive at an average rate of 15 per hour following a Poisson distribution. NOTE: calculate the measures per hour. Calculate system utilization. (Round your answer to the nearest whole percent without the percent sign.) System Utilization =
Answer:
System utilization = 0.7 or 70%
Step-by-step explanation:
Given arrival rate of customer = 15 customer/Hour
Servie rate = [tex] \dfrac{60}{2.8} customer/Hour [/tex]
Now, use the below formula to find the system utilization.
System utilization = [tex] \dfrac{\text{ Arrival rate of customer }}{\text{ Servie rate}}[/tex]
System utilization = [tex] \dfrac{15}{ \dfrac{60}{2.8}}[/tex]
System utilization = [tex] \dfrac{15}{ \dfrac{60}{2.8}}[/tex]
System utilization = 0.7 or 70%
Given two dependent random samples with the following results: Population 1 76 77 66 71 55 63 83 58 Population 2 78 71 71 65 61 71 77 62 Can it be concluded, from this data, that there is a significant difference between the two population means? Let d=(Population 1 entry)−(Population 2 entry). Use a significance level of α=0.1 for the test. Assume that both populations are normally distributed. Step 2 of 5: Find the value of the standard deviation of the paired differences. Round your answer to one decimal place.
Answer: Std = 6.0
Step-by-step explanation:
Let us take a step by step process to solve this problem.
We have from the question that;
Population 1: 76 77 66 71 55 63 83 58
Population 2: 78 71 71 65 61 71 77 62
where n is no of occurrence = 8
taking the difference of P1 - P2 we have;
Difference (d) : -2 6 -5 6 -6 -8 6 -4
Total value of difference = -7
Difference squared (d₁ -d)² = 4 36 25 36 36 64 36 16
Total value of difference squared (d₁ -d)² = 253
The mean Σ = sum of values (d)/total value = -7/8 = -0.875
⇒ We are asked to find the value of the standard deviation of the paired difference.
Standard deviation is given as;
Std = √(Σ (Δd)² / n-1
Std = √[(253) / 8-1]
Std = √(253/7) = 6.0
Std = 6.0
cheers i hope this helped!!!!!!
Match the expressions given in words with their values when m = 6. 42 3 21 15 2 the difference of the product of 3 and m minus the quotient of m divided by 2 arrowRight the sum of 3 times m and 4 times m arrowRight the quotient of 6 divided by the difference of m minus 3 arrowRight the sum of m and 3 divided by the difference of m minus 3 arrowRight
Answer:
154223Step-by-step explanation:
When m=6
(1) The difference of the product of 3 and m minus the quotient of m divided by 2
[tex]3m-\dfrac{m}{2}\\=3(6)- \dfrac{6}{2}\\=18-3\\=15[/tex]
(2)The sum of 3 times m and 4 times m
3m+4m
=3(6)+4(6)
=18+24
=42
(3)The quotient of 6 divided by the difference of m minus 3
[tex]\dfrac{6}{m-3} =\dfrac{6}{6-3} =\dfrac{6}{3} =2[/tex]
(4)The sum of m and 3 divided by the difference of m minus 3
[tex]\dfrac{m+3}{m-3}= \dfrac{6+3}{6-3}=\dfrac{9}{3}=3[/tex]
The volume of a cube is 343 cubic inches. What is the length of each edge of the cube?
Answer:7 inches
Step-by-step explanation:
Volume of cube=343
volume of cube=length x length x length
length =L
Volume of cube=LxLxL
343=L^3
L^3=343
Taking the cube root of both sides we get
L=cube root of 343
L=7
Length =7 inches
Anna has 7 pairs of yellow socks, 8 pairs of red socks, and 2 pairs of blue socks mixed together in a drawer. All pairs of socks are identical except for their colors. What is the smallest number of socks she has to take out without looking to make sure she has 2 matching pairs of socks
To ensure Anna has two matching pairs of socks, she will need to draw out five socks. This illustrates a principle in probability known as the Pigeonhole Principle.
Explanation:In this mathematics question, we are dealing with an example of the Pigeonhole Principle. Anna has 3 different types of socks: yellow, red, and blue. In the worst-case scenario, she picks one of each color for the first three socks- this doesn't give her a pair. To ensure she gets a pair, she would need to take out a fourth sock. Since we only have three different types, this fourth sock will have to be either a yellow, red or blue one, thus ensuring at least one pair. However, the question asks for two pairs. This would involve picking out a fifth sock, in the worst-case scenario this fifth sock could match with the second pair. Hence, to guarantee that there are two matching pairs, she would need to draw out a total of five socks.
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Una goma tiene un diámetro de 18 pulgadas. Cual es el área de la goma en pulgadas cuadradas?
Answer:
The area of the car tire = 254.57 in²
el área de la goma en pulgadas cuadradas = 254.57 in²
Step-by-step explanation:
English Translation
A car tire has a diameter of 18 inches which is the area of the tire in square inches?
A car tire is circular in nature, the area of a circle (car tire) is given as
A = πr²
where
π = pi (a constant) = (22/7)
r = radius of the circle = (diameter/2) = (18/2) = 9 inches
Area of the car tire = π×9² = 254.57 in²
Hence, the area of the car tire = 254.57 in²
Hope this Helps!!!
Mr. Hobbs has 10 blue markers, 6 black markers, and 8 red markers
on his desk. What fraction of black markers can be found on Mr.
Hobbs' desk?
Select one:
1.3/9
2.5/12
3.1/4
4.1/3
Answer:
4
Step-by-step explanation:
Im not completely sure
Suppose the true proportion of students at a college who study abroad is 0.25. I select a random sample of 40 students from the college and record if they have studied abroad. What is the probability that the proportion of students in my sample who have studied abroad is less than 0.2
Answer:
[tex]\mu_{\hat p} = 0.25[/tex]
[tex]\sigma_{\hat p}= \sqrt{\frac{0.25*(1-0.25)}{40}}= 0.0685[/tex]
[tex] z = \frac{0.2-0.25}{0.0685}= -0.730[/tex]
And we can use the normal standard distribution or excel to find this probability and we got:
[tex] P(\hat p <0.2) = P(z<-0.730)= 0.233[/tex]
Step-by-step explanation:
We define the parameter as the proportion of students at a college who study abroad and this value is known [tex]p =0.25[/tex], we select a sample size of n =40 and we are interested in the probability associated to the sample proportion, but we know that the distirbution for the sample proportion is given by:
[tex]\hat p \sim N(p , \sqrt{\frac{p(1-p)}{n}}[/tex]
And the paramters for this case are:
[tex]\mu_{\hat p} = 0.25[/tex]
[tex]\sigma_{\hat p}= \sqrt{\frac{0.25*(1-0.25)}{40}}= 0.0685[/tex]
We want to find the following probability:
[tex]P(\hat p< 0.2)[/tex]
For this case since we know the distribution for the sample proportion we can use the z score formula given by:
[tex] z = \frac{\hat p -\mu_{\hat p}}{\sigma_{\hat p}}[/tex]
Replacing the info given we got:
[tex] z = \frac{0.2-0.25}{0.0685}= -0.730[/tex]
And we can use the normal standard distribution or excel to find this probability and we got:
[tex] P(\hat p <0.2) = P(z<-0.730)= 0.233[/tex]
To find the probability that the proportion of students in your sample who have studied abroad is less than 0.2, you can use the normal distribution approximation for sampling proportions.
Explanation:To find the probability that the proportion of students in your sample who have studied abroad is less than 0.2, you can use the normal distribution approximation for sampling proportions. First, find the mean of the sampling distribution, which is equal to the true proportion (0.25) multiplied by the sample size (40), giving a mean of 10.
Next, find the standard deviation of the sampling distribution, which is calculated as the square root of (p(1-p)/n), where p is the true proportion (0.25) and n is the sample size (40). The standard deviation is approximately 0.071.
Finally, use the normal distribution to find the probability that the proportion is less than 0.2. Using the z-score formula, calculate the z-score as (sample proportion - mean)/(standard deviation). In this case, the z-score is approximately -1.41. Use a standard normal distribution table or calculator to find the corresponding probability, which is approximately 0.079.
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According to the U.S. Department of Transportation’s Air Travel Consumer Report, the nation’s 12 largest airlines recorded an on-time arrival percentage of 77.4% during 2001. Of interest is to estimate the mean delay time for all flights that did not arrive on time during 2013. A simple random sample of 35 late arriving flights was selected, and the mean delay time of this sample of 35 flights was 14.2 minutes, with a standard deviation (s) of 6.4 minutes. Use this information to calculate and interpret a 95% confidence interval for the mean delay time for all flights that did not arrive on time during 2013.
Answer:
[tex]14.2-2.03\frac{6.4}{\sqrt{35}}=12.004[/tex]
[tex]14.2+2.03\frac{6.4}{\sqrt{35}}=16.396[/tex]
We are 95% confidence that the true mean for the delay time is between (12.004 and 16.396)
Step-by-step explanation:
Information given
[tex]\bar X=14.2[/tex] represent the sample mean for the delay time
[tex]\mu[/tex] population mean
s=6.4 represent the sample standard deviation
n=35 represent the sample size
Confidence interval
The confidence interval for the true parameter of interest is given by:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom, given by:
[tex]df=n-1=35-1=34[/tex]
The Confidence level is 0.95 or 95%,and the significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value for this case is [tex]t_{\alpha/2}=2.03[/tex]
And replacing we got:
[tex]14.2-2.03\frac{6.4}{\sqrt{35}}=12.004[/tex]
[tex]14.2+2.03\frac{6.4}{\sqrt{35}}=16.396[/tex]
We are 95% confidence that the true mean for the delay time is between (12.004 and 16.396)
The traveler is disputing the claim about the variance. The hypothesis test is a right-tailed test. The result of the test does not provide enough evidence to dispute the airline's claim.
Explanation:109. The traveller is disputing the claim about the variance.
110. A sample standard deviation of 15 minutes is the same as a sample variance of 225 minutes.
112. H-o: The variance is 150 minutes or less.
113. d-f = 24
114. chi-square test statistic = 35.172
115. p-value = 0.082
116. Graph the situation:
Horizontal axis: VarianceMean: 150 minutesTest statistic: 225 minutesShade the p value: right tail117. Let a = 0.05
Decision: Fail to reject the null hypothesis
Conclusion: There is not enough evidence to dispute the airline's claim about the variance being 150 minutes or less.
Learn more about Hypothesis testing here:https://brainly.com/question/34171008
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One grocery clerk can stock a shelf in 40 min. A second clerk requires 25 min to stock the same shelf. How long would it take to stock the shelf if the two clerks worked together?
Answer:
It would take 15.3846 minutes to stock the shelf if the two clerks worked together
Step-by-step explanation:
The first grocery clerk can stock a shelf in 40 minutes, it means that he can do 1/40 shelf per minute. At the same way, the second clerk requires 25 minutes, it means that he can do 1/25 shelf per minute
Then, if they worked together, they can stock 13 shelfs in 200 minutes, and it is calculated as:
[tex]\frac{1}{40}+\frac{1}{25} = \frac{13}{200}[/tex]
Now, using the rule of three, we need to find the minutes required to stock 1 shelf if they work at a rate of 13 shelf in 200 minutes as:
13 shelfs -------------- 200 minutes
1 shelf --------------- X minutes
Where X are the minutes required to stock 1 shelf.
So, solving for X, we have:
[tex]X=\frac{1*200}{13}=15.3846[/tex]
Finally, it would take 15.3846 minutes to stock the shelf if the two clerks worked together
help. If 20 men can survive for 24 days on 15 cans of rations, how many cans will be needed for 16 men to survive for 36 days?
Answer: 29 cans.
Step-by-step explanation:
20 can survive 24 days with 15 cans.
If X is the number of days that a man can survive with one can of rations.
so X is in the units can/day
then we have that:
24/15*X = 20
X = 20*15/24 = 12.5
This means that a man can live 12.5 days with a can of food.
then, for 16 men and 36 days we have:
(36/C)*12.5 = 16
C = (36/16)*12.5 = 28.1215
And we can not have a 0.1215 of a can, so we should round it up to 29 cans.
The mortgage department of a large bank is interested in the nature of loans of first-time borrowers. This information will be used to tailor their marketing strategy. They believe that 40% of first-time borrowers take out smaller loans than other borrowers. They perform a hypothesis test to determine if the percentage is the same or different from 40%. They sample 100 first-time borrowers and find 53 of these loans are smaller than the other borrowers. For the hypothesis test, they choose a 5% level of significance. What would be the null and alternative hypotheses
Answer:
Step-by-step explanation:
The null hypothesis is the statement or claim that is believed or assumed to be true. In this case, the null hypothesis is "They believe that 40% of first-time borrowers take out smaller loans than other borrowers". Since we are dealing with proportion, we will denote it with p. The null hypothesis would be
p = 0.4
The alternative hypothesis is what the researcher expects or predicts. It is the statement that is believed to be true if the null hypothesis is rejected. The alternative hypothesis is "They perform a hypothesis test to determine if the percentage is the same or different from 40%". It would be written as
p ≠ 0.4
A government official is in charge of allocating social programs throughout the city of Vancouver. He will decide where these social outreach programs should be located based on the percentage of residents living below the poverty line in each region of the city. He takes a simple random sample of 125 people living in Gastown and finds that 25 have an annual income that is below the poverty line.
Part i) The proportion of the 125 people who are living below the poverty line, 25/125, is which of the following:________.
A. variable of interest.
B. parameter.
C. statistic.
Part ii) Use the sample data to compute a 95% confidence interval for the true proportion of Gastown residents living below the poverty line.
(Please carry answers to at least six decimal places in intermediate steps. Give your final answer to the nearest three decimal places).
95% confidence interval = ( ___ , ___ )
Answer:
Part I: C. statistic
Part II: 95% confidence interval = (0.130, 0.270)
Step-by-step explanation:
Part I: The proportion of the 125 people who are living below the poverty line, 25/125, is which of the following: statistic, as it is a measure taken from the sample.
Part II:
We have to calculate a 95% confidence interval for the proportion.
The sample proportion is p=0.2.
[tex]p=X/n=25/125=0.2[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.2*0.8}{125}}\\\\\\ \sigma_p=\sqrt{0.00128}=0.035777[/tex]
The critical z-value for a 95% confidence interval is z=1.96.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=1.96 \cdot 0.035777=0.070122[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sisgma_p = 0.2-0.070122=0.129878\\\\UL=p+z \cdot \sisgma_p = 0.2+0.070122=0.270122[/tex]
The 95% confidence interval for the population proportion is (0.130, 0.270).