Answer:
a. .92
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error of the interval is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The lower bound is the point estimate [tex]\pi[/tex] subtracted by the margin of error.
The upper bound is the point estimate [tex]\pi[/tex] added to the margin of error.
Point estimate:
The confidence interval is symmetric, so it is the mean between the two bounds.
In this problem:
[tex]\pi = \frac{0.372 + 0.458}{2} = 0.415[/tex]
Sample of 400, which means that [tex]n = 400[/tex]
Margin of error is the estimate subtracted by the lower bound. So [tex]M = 0.415 - 0.372 = 0.043[/tex]
We have to find z.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.043 = z\sqrt{\frac{0.415*0.585}{400}}[/tex]
[tex]z = \frac{0.043\sqrt{400}}{\sqrt{0.415*0.585}}[/tex]
[tex]z = 1.745[/tex]
[tex]z = 1.745[/tex] has a pvalue of 0.96.
This means that:
[tex]1 - \frac{\alpha}{2} = 0.96[/tex]
[tex]\frac{\alpha}{2} = 1 - 0.96[/tex]
[tex]\frac{\alpha}{2} = 0.04[/tex]
[tex]\alpha = 0.08[/tex]
Confidence level:
[tex]1 - \alpha = 1 - 0.08 = 0.92[/tex]
So the correct answer is:
a. .92
To determine the confidence coefficient for the proportion of MSU students who attended at least three football games, the margin of error is calculated from the given interval range and related to the Z-value of a standard normal distribution. The coefficient that matches the margin of error from the calculation is approximately 0.95, indicating a 95% confidence level.
The confidence interval for the proportion of Michigan State University (MSU) students who attended at least three football games is given as (0.372, 0.458). To determine the confidence coefficient used to calculate this interval, we need to look at the width of the interval and how it relates to the standard error of the proportion.
The width of the confidence interval is 0.458 - 0.372 = 0.086. Since we know that the total width of the interval spans the range of twice the margin of error, one margin of error is then 0.086 / 2 = 0.043.
Using the Z-table for the normal distribution, we can find which confidence coefficient corresponds to a Z-value that gives a margin of error of 0.043, considering that the formula for the margin of error in this case would be: Z * sqrt((p*(1-p))/n). For a sample size of 400, and approximating p by the midpoint of the confidence interval (0.372 + 0.458)/2 = 0.415, the computation would look roughly like this:
Z * sqrt((0.415*(1-0.415))/400) = 0.043
After solving this equation for Z, we can then locate the corresponding confidence level on the standard normal (Z) distribution table. This process would lead to finding that the closest confidence coefficient that would generate the margin of error of 0.043 with the given sample size and point estimate proportion is approximately 0.95, or 95%.
Therefore, the confidence coefficient is 0.95, which corresponds to option b. 0.95.
What is 2015722184 multiplied by 142748261654 i cant find this on calculator for some reason
Answer:
The Exact answer is 287740837743404332336.
The Decimal Answer is 2.87740837 ⋅ 10 ^20.
A local movie theater is increasing ticket pricesby 10%. If a student ticket originally cost $8.50,how much will the theater be adding to the priceof the ticket?
A. $0.10
B. $0.85
C. $1.50
D. $9.35
Answer:
B
Step-by-step explanation:
Because since they are increasing $8.50 by 10% you got to divide by 10 to get the answer. Because 10% is equal as multiplying .10 or dividing by 10. So when you divide by 10 you get 0.85. So B is the answer to the question.
The scores of individual students on the American College Testing (ACT), college readiness assessment, have a Normal distribution with a mean of 18.6 and a standard deviation of 6.0. At Northside High, 36 seniors take the test. Assume the scores at this school have the same distribution as national scores. What is the standard deviation of the sampling distribution of the sample mean score for a random sample of 36 students
Answer:
The standard deviation of the sampling distribution of the sample mean score for a random sample of 36 students is 1.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
[tex]\sigma = 6, n = 36[/tex]
Then, by the Central Limit Theorem:
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]s = \frac{6}{\sqrt{36}}[/tex]
[tex]s = 1[/tex]
The standard deviation of the sampling distribution of the sample mean score for a random sample of 36 students is 1.
grammium-the metal billings used to make the statuettes-is a mixture of aluminum and zinc. each atom of aluminum has 13 protons. that's 3 more than 1/3 the number, z, of protons in an atom of zinc. write and solve an equation to find z
Which of the following statements about ANOVA completely randomized design is correct? a. The ANOVA test assumes that the sampled populations are normally distributed. b. The ANOVA test assumes that the sampled populations have a common variances . c. The ANOVA test assumes that the samples are randomly and independently selected from their respective populations. d. All of these. e. None of these.
Answer:
d. All of these.
Step-by-step explanation:
Analysis of variance (ANOVA) is used in statistics to determine the difference between the mean of two groups. A completely randomized design implies that samples are randomly assigned to either a treatment group or a placebo group during the experiment. For example, if 40 people are selected to test the effect of an analgesic, four groups could be designed- Groups A, B, C, and D. Groups A, B, and C, can be given different amounts of the drug and Group D, given a placebo. This is an example of a randomized design because the participants were randomly assigned to the groups.
For an ANOVA test to exhibit complete randomized design, we assume that the sample populations are normally distributed, and also have the same variances. We also assume in this design, that samples are randomly and independently selected from their respective populations.
what is the sum in simplest form?
4 1/2 + 1 3/5
To find the sum in simplest form of 4 1/2 and 1 3/5, you convert each to an improper fraction, adding the fractions and convert back to a mixed number. The sum is 6 1/10.
Explanation:The sum in simplest form of the two numbers 4 1/2 and 1 3/5 can be calculated as follows:
Change each mixed number into an improper fraction. 4 1/2 becomes 9/2 and 1 3/5 becomes 8/5.Then add the two fractions: 9/2 + 8/5 equals 45/10 + 16/10 (after finding a common denominator), which equals 61/10.Finally, convert back to a mixed number to get 6 1/10.So, the sum in the simplest form of 4 1/2 and 1 3/5 is 6 1/10.
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Explore the area of sectors of circles by following these steps.
1. What is the area of circle
Check
Answer: 9pi
Step-by-step explanation:
If a sunspot has a temperature of 3900 K and the photosphere of the Sun has a temperature of 5760 K, how many times
brighter per unit area is the photosphere than the sunspot?
The photosphere is approximately 5.62 times brighter per unit area than the sunspot.
Stefan-Boltzmann Law: We'll use the Stefan-Boltzmann Law, which states that the radiant emittance (power emitted per unit area) of a black body is proportional to the fourth power of its absolute temperature (T). Mathematically, this can be expressed as:
M = σ * T^4
Where:
M is the radiant emittance (W/m²)
σ is the Stefan-Boltzmann constant (5.670374 x 10^-8 W m^-2 K^-4)
T is the absolute temperature (Kelvin)
Radiant Emittance: Calculate the radiant emittance of the sunspot and the photosphere using their respective temperatures:
Sunspot: M_sunspot = σ * T_sunspot^4 = 5.670374e-8 * 3900^4 ≈ 83.32 x 10^12 W/m²
Photosphere: M_photosphere = σ * T_photosphere^4 = 5.670374e-8 * 5760^4 ≈ 468.37 x 10^12 W/m²
Brightness Ratio: Calculate the ratio of the photosphere's radiant emittance to the sunspot's radiant emittance to determine how much brighter the photosphere is per unit area:
Brightness Ratio = M_photosphere / M_sunspot ≈ 468.37 x 10^12 W/m² / 83.32 x 10^12 W/m² ≈ 5.62
Therefore, the photosphere is approximately 5.62 times brighter per unit area than the sunspot.
Below are boxplots that summarize the weights (in pounds) of large samples from two breeds of dog: the Anatolian Shepherd and the Black Russian Terrier. (a) Compare the distributions of weights for the two dog breeds. (b) This sample of Black Russian Terriers does not contain any outliers. What weights would a Black Russian Terrier have to be to be considered an outlier
Answer:
(a) The median of both plots is same, 120 pounds is the median weight of Anatolian Shepherd and the Black Russian Terrier breed.
The range of both plots is also same that is 75 pounds.
The box plot of Anatolian Shepherd is skewed towards left therefore, it is considered to be positively distributed.
The box plot of Black Russian Terrier is skewed towards right therefore, it is considered to be negatively
(b) Any data point which is greater than 155 or smaller than 80 will be considered an outlier.
Step-by-step explanation:
A box plot is a graph which shows five statistical characteristics of a data set.
1. Maximum value
2. Minimum value
3. Median
4. Upper Interquartile
5. Lower interquartile
(a) Compare the distributions of weights for the two dog breeds
Please refer to the attached diagram of the question.
The median of both plots is same, 120 pounds is the median weight of Anatolian Shepherd and the Black Russian Terrier breed.
The range of Anatolian Shepherd is,
Range = Maximum value - Minimum value
Range = 175 - 100 = 75 pounds
The range of Black Russian Terrier is,
Range = Maximum value - Minimum value
Range = 155 - 80 = 75 pounds
Therefore, the range of both plots is also same that is 75 pounds.
A box-plot is considered to be normally distributed when the median is at the center of upper quartile and lower quartile.
The box plot of Anatolian Shepherd is skewed towards left therefore, it is considered to be positively distributed.
The box plot of Black Russian Terrier is skewed towards right therefore, it is considered to be negatively distributed.
(b) What weights would a Black Russian Terrier have to be to be considered an outlier?
An outlier is a data point in the data set that is very different from the other data points.
In this case, the maximum and minimum values in the Black Russian Terrier box-plot are
Maximum = 155
Minimum = 80
Therefore, any data point which is greater than 155 or smaller than 80 will be considered an outlier.
To compare the distributions of weights for the Anatolian Shepherd and Black Russian Terrier, we can look at the boxplots provided. If a Black Russian Terrier were to be considered an outlier, its weight would be significantly different from the other weights in the sample.
Explanation:To compare the distributions of weights for the Anatolian Shepherd and Black Russian Terrier, we can look at the boxplots provided. The boxplot for each breed shows the minimum value, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum value. We can compare the positions of these measures to determine the differences between the two breeds.
If a Black Russian Terrier were to be considered an outlier, its weight would be significantly different from the other weights in the sample. An outlier is typically defined as a value that is more than 1.5 times the interquartile range (IQR) above the upper quartile (Q3) or below the lower quartile (Q1). To find the weight that would be considered an outlier for Black Russian Terriers, we need to calculate the IQR and use it to determine the threshold for outliers.
A restaurant has 10 sodas that come in 12 different cup sizes. How many different drinks can you order?
Answer:
There are 120 different drinks that you can order.
Step-by-step explanation:
You have 10 options of soda for which you can choose.
For each options, there are 12 different cup sizes.
12*10 = 120
So there are 120 different drinks that you can order.
A study was conducted to investigate the effectiveness of hypnotism in reducing pain. An SRS of 8 subjects was randomly selected, and the pain level was recorded for each one, with a lower score indicating less pain. After the subjects were hypnotized, their pain level was recorded again. The researchers calculated the difference in the pain level for each subject, calculated as After – Before. Assume the differences follow an approximately normal distribution, with the following sample statistics: Is pain, on average, lower after hypnotism? Test at a 1% significance level. a. The assumptions for this test are not met because the sample size is too small. b. Yes, the p-value is less than 0.01, so there is sufficient evidence at the 0.01 level to conclude that pain levels are lower after hypnotism. c. Yes, the p-value is greater than 0.01, so there is sufficient evidence at the 0.01 level to conclude that pain levels are lower after hypnotism. d. No, the p-value is less than 0.01, so there is insufficient evidence at the 0.01 level to conclude that pain levels are lower after hypnotism. e. No, the p-value is greater than 0.01, so there is insufficient evidence at the 0.01 level to conclude that pain levels are lower after hypnotism. 3 points Save Answer
Answer:
e. No, the p-value is greater than 0.01, so there is insufficient evidence at the 0.01 level to conclude that pain levels are lower after hypnotism.
Step-by-step explanation:
Hello!
The study's objective is to test if hypnotism reduces pain.
A sample of n=8 subjects was taken and the pain level was recorded in each subject before and after being hypnotized.
The variable of interest was determined by calculating the difference of pain level after - before hypnosis. This is a paired sample test and the variable can be determined as:
Xd: Difference between pain level felt after hypnosis and pain level felt before hypnosis of a subject.
The sample average and standard deviation obtained were:
Xd= -3
Sd= 3
And the variable is presumed to be approximately normal.
An approximately normal distribution is enough to conduct a paired sample t-test.
If the claim is that hypnosis reduces pain, then the average pain level after hypnosis should be less than the average pain level before hypnosis, then the average difference is expected to be negative, symbolically: μd < 0
The test will be one-tailed and so will be the p-value.
Remember: The p-value is defined as the probability corresponding to the calculated statistic if possible under the null hypothesis (i.e. the probability of obtaining a value as extreme as the value of the statistic under the null hypothesis).
So first step is to calculate the value of the statistic under the null hypothesis and then you can calculate the p-value.
H₀: μd ≥ 0
H₁: μd < 0
[tex]t_{H_0}= \frac{X_d-Mu_{d}}{\frac{S_d}{n} }= \frac{-0-0}{\frac{3}{\sqrt{8} } } = -2.828= -2.83[/tex]
The DF of the t-test are n-1= 7
Then you can calculate the p-value as:
P(t₇≤-2.83)= 0.0127
The level of the test is α: 0.01
The decision rule is:
If p-value ≤ α, reject the null hypothesis.
If p-value > α, do not reject the null hypothesis.
The p-value > α the decision is to not reject the null hypothesis.
Correct option: e. No, the p-value is greater than 0.01, so there is insufficient evidence at the 0.01 level to conclude that pain levels are lower after hypnotism.
I hope this helps!
what is the median for 460,470,480,480,480,490,490,490,490,490,500,500,510
Answer:
490
Step-by-step explanation:
The Median is the middle number in the set. In this case, it is 490.
~
Answer:
490
Step-by-step explanation:
the median is simply the middle number, and if there are two, you would add them together then divide whatever the total of those two numbers are by two, like this (4+5)/2
Gauges are used to reject all components for which a certain dimension is not within the specification 1.5 d . It is known that this measurement is normally distributed with mean 1.5 and standard deviation 0.2. Determine the value d such that the specifications cover 95% of the measurements.
The value of 'd' such that the specifications cover 95% of the measurements can be determined using the z-score corresponding to a 95% confidence interval, and is found to be 0.392 by multiplying with the known standard deviation.
Explanation:In this case, you're looking to find the value for d such that specifications cover 95% of the measurements. We know that the measurements follow a normal distribution, with a mean of 1.5 and a standard deviation of 0.2.
According to the Empirical Rule (for a bell-shaped, symmetric distribution), approximately 95 percent of the data is within two standard deviations of the mean. Here, however, we want to find the distance d from the mean that encapsulates 95% of the data. We already know that d falls within a 95% confidence interval, which splits the excluded 5% evenly between the upper and lower tails of the distribution.
So, we will use a z-score corresponding to 95% of the measurements. The z-score corresponding to 95% is approximately 1.96 (covering 2.5% in each tail). Multiply this z-score by the standard deviation to get the value of d (1.96 * 0.2 = 0.392). Thus, d = 0.392 should be the value that ensures the specifications cover 95% of the measurements.
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Todd has $124 in his checking account. He wrote two checks for $13.96 and $21.67 and transferred
$14 into his checking from his savings.
What is his new balance?
Answer:
$[tex]74.37[/tex]
Step-by-step explanation:
To figure out how much is left in his checking account, simply subtract the amount he took out.
[tex]124 -13.96 = 110.04[/tex]
[tex]110.04 - 21.67 =88.37[/tex]
[tex]88.37 - 14= 74.37[/tex]
$[tex]74.37[/tex] is left in his checking account.
Answer:
$102.37
Step-by-step explanation:
Todd has $124 to begin with
He writes two checks (subtract) $13.96 & $21.67
Then he removes $14.00 from his savings & places it into his Checking. (Adding) it to his checking account balance
$124-13.96-21.67+14 = $102.37
Which of the following is NOT a perfect square? Question 3 options: 36 25 49 81 35 144 100
Answer:
35
Step-by-step explanation:
Answer:
35
Step-by-step explanation:
Lee and Maya are collecting leaves for an art project. Lee collect 24/100 of the tiral number of leaves needed. Maya collects 4/10 of the total number of leaves needed. What fraction of tge total number of leaves did they collect altogether?
Answer:
The fraction of the total number of leaves did they collect altogether is [tex]\frac{16}{25}[/tex]
Step-by-step explanation:
This question can be solved by a sum of fractions.
Lee collect 24/100 of the tiral number of leaves needed.
Maya collects 4/10 of the total number of leaves needed.
What fraction of the total number of leaves did they collect altogether?
This is the sum of 24/100 and 4/10.
The lesser common multiple between 100 and 10 is 100. So
[tex]\frac{24}{100} + \frac{4}{10} = \frac{24 + 10*4}{1001} = \frac{64}{100}[/tex]
We can simplify by four
The fraction of the total number of leaves did they collect altogether is [tex]\frac{16}{25}[/tex]
Final answer:
Lee and Maya have collected 64/100 or 64% of the total number of leaves needed for their project when we add Lee's 24/100 and Maya's 40/100 together.
Explanation:
Lee has collected 24/100 of the leaves, and Maya has collected 4/10 of the leaves for their art project. To find out what fraction they have collected altogether, we need to add the two fractions. However, before we can do that, we need to make sure the fractions have the same denominator.
Since 4/10 can be simplified to 40/100, we now have a common denominator of 100. Adding the two fractions together:
Lee's leaves: 24/100
Maya's leaves: 40/100
Total leaves collected: 24/100 + 40/100 = 64/100
Therefore, Lee and Maya have collected 64/100 of the total number of leaves needed for their project.
Hi there! I´m new ¿Can you help me please?
A fence post that is 2 meters tall casts a shadow of 1.6 meters. How tall is a tree that castsa shadow of 24 meters?
I AM A EIGHT GRADER !
Answer:
look below im smart and im just a seventh grader O w O
Step-by-step explanation:
2f(1.6m)
X=24
X=2*24/1.6
X=2*15
X= 30 m
What is the exact decimal equivalent of 7/12
what is 20 plus 2 /6
Answer:
[tex] \frac{61}{3} = 20 \frac{1}{3} [/tex]
Step-by-step explanation:
[tex]20 + \frac{2}{6} [/tex]
[tex] \frac{2}{6} = \frac{2 \div 2}{6 \div 2} = \frac{1}{3} [/tex]
[tex]20 + \frac{1}{3} = \frac{20}{1} + \frac{1}{3} = \frac{20 \times 3}{1 \times 3} + \frac{1}{3} [/tex]
[tex] \frac{60}{3} + \frac{1}{3} = \frac{60 + 1}{3} = \frac{61}{3} [/tex]
[tex] \boxed{\green{= \frac{61}{3} = 20 \frac{1}{3}}} [/tex]
rewrite the equation by completing the square x^2+x-72=0
Answer:
(x + 1/2) ² = 289/4
Step-by-step explanation: I answered this correctly
The solutions to t[tex]x^2 + x = 72[/tex]he equation [tex]x^2 + x - 72[/tex] = 0 are x = 8 and x = -9.
To rewrite the quadratic equation[tex]x^2 + x - 72[/tex] = 0 by completing the square, we follow these steps:
Step 1: Move the constant term to the other side of the equation:
[tex]x^2 + x = 72[/tex]
Step 2: Take half of the coefficient of the x-term (which is 1) and square it. Add this value to both sides of the equation:
[tex]x^2 + x + (1/2)^2 = 72 + (1/2)^2\\x^2 + x + 1/4 = 72 + 1/4[/tex]
Step 3: Rewrite the left side as a perfect square:
[tex](x + 1/2)^2 = 289/4[/tex]
Step 4: Take the square root of both sides:
x + 1/2 = ± √(289/4)
Step 5: Solve for x:
x + 1/2 = ± 17/2
x = -1/2 ± 17/2
x = (-1 + 17)/2 or x = (-1 - 17)/2
x = 16/2 or x = -18/2
x = 8 or x = -9
The solutions to the equation [tex]x^2 + x - 72[/tex] = 0 are x = 8 and x = -9.
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What is the value of x
Answer: The answer is b
Step-by-step explanation:
The answer is b due to the exterior angle theorem which is 1 exterior angles = 2 interior angles on the opposites sides
so the eqaution is
105= 67+x
and x + 38 which is b
Answer:
C. 33
Step-by-step explanation:
use a protractor in the future
Teddy uses 2.5 gallons of ice to fill 4 buckets.he needs to fill 30 buckets.how many gallons of ice will teddy need?
Answer:
48- Teddy will need 48 gallons of ice.
Step-by-step explanation:
2.5 ÷ 4 = 1.6
1.6 x 30 = 48!
Teddy will need 48 gallons of ice.
Hope i helped ^^
Simplify this complex fraction
Answer:
2/ 21
Step-by-step explanation:
2/3 ÷ 7
Copy dot flip
2/3 * 1/7
2/ 21
A basketball has a diameter of 9.5 inches what is the volume of the basketball using 3.14 for pi.
Answer:
448.69 in^3
Step-by-step explanation:
The volume of a sphere is given by the formula ...
V = (4/3)πr^3
We want to use diameter, so we can substitute r = d/2 into the formula:
V = (4/3)π(d/2)^3 = (4/(3·8))πd^3
V = (π/6)d^3
For the given numbers, ...
V = (3.14/6)(9.5^3) ≈ 448.69 in^3 . . . . volume of a basketball
how to subtract fractons with unlike denominators
Answer:
so first you cross multiply the first fractions' numerator by the other fractions denominator.
and then you do the same for the other one
then you multiply both denominators
the answer u got from cross multiplying, you get those numbers and subtract
them. the denominator doesn't need anything done to it.
Step-by-step explanation:
hope it helps (pls brainliest if u can)
What is the greatest prime factor of [4²]² -1?
Using the formula
[tex]a^2-b^2=(a+b)(a-b)[/tex]
We can write
[tex](4^2)^2-1 = 16^2-1 = (16+1)(16-1)=17\cdot 15[/tex]
Since 17 is prime and the factors of 15 are 3 and 5, the three prime factors of this number are 3, 5 and 17.
The required prime factors of the given expressions are given as 3, 5, and 17.
What are the factors?A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.
Here,
Given expression,
=[4²]² -1
= 16² - 1
Since (a² - b²) = (a + b)(a - b)
= (16 + 1)(16 - 1)
= 17 × 15
= 17 × 3 × 5
Thus, the required prime factors of the given expressions are given as 3, 5, and 17.
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What is the equation of the line passing through the points (2, -1) and (5.-10) in slope-intercept form
O y=-3x-5
O y=-3x+5
Oy - 3x-5
O y=3x+5
Answer:
y = -3x + 5
Step-by-step explanation:
Usually by drawing a simple graph, you can tell what the equation is, even if the graph isn't 100% accurate. From the points alone, you can tell that the slope is negative, since as you increase in x you decrease in y (which is a negative relationship). You can tell that it's +5 rather than -5 because the graph sketched shows that the line goes above 0 (indicating a positive number), rather than below (a negative number).
The slope of the line through points (2, -1) and (5,-10) is -3. With y-intercept +5, the line's equation in slope-intercept form is y = -3x + 5.
Explanation:The subject of your question is in the field of Mathematics, specifically algebra.
You are looking for the equation of the line in slope-intercept form, which is y = mx + b where m is the slope and b is the y -intercept. We first calculate the slope using the formula (y2 - y1) / (x2 - x1). Plugging in the values we get, m = (-10 - (-1)) / (5 - 2) = -9 / 3 = -3. Thus, m = -3. Then, to find the y-intercept, we use the point-slope form of a line equation y - y1 = m(x - x1), and plug in one of the points (2, -1) and the slope value, and then solve for b. The equation in slope-intercept form will be y = -3x + 5.
So the answer to your question is y = -3x + 5.
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Suppose a recent nationwide survey showed that 35% of American college students have traveled outside of the USA. But a well known university believes its students have traveled abroad more than the national rate of 35%. A random sample of 100 students from this university had 42 students who have traveled outside the USA. A hypothesis test is then conducted to determine if we can believe that, statistically, more of this university's students have traveled abroad. Using these numbers, what is the value of the test statistic for this hypothesis test
Answer:
Step-by-step explanation:
We would set up the hypothesis test.
For the null hypothesis,
p = 0.35
For the alternative hypothesis,
p > 0.35
This is a right tailed test considering the > in the alternative hypothesis.
Considering the population proportion, probability of success, p = 0.35
q = probability of failure = 1 - p
q = 1 - 0.35 = 0.65
Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 42
n = number of samples = 100
P = 42/120 = 0.42
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.42 - 0.35)/√(0.35 × 0.65)/100 z = 1.48
The test statistic for the hypothesis test, given a sample proportion of 0.42, hypothesized population proportion of 0.35, and sample size of 100 students, is calculated to be 1.47.
To calculate the test statistic for the hypothesis test, we use the formula for testing a proportion:
Calculate the sample proportion (\(\hat{p}\)): \(\hat{p} = \frac{x}{n}\), where x is the number of students who have traveled abroad in the sample and n is the sample size.Calculate the standard error (SE) of the sample proportion using the formula: SE = \(\sqrt{\frac{p(1-p)}{n}}\), where p is the hypothesized population proportion.Compute the test statistic (z) by subtracting the hypothesized proportion from the sample proportion and dividing the result by the standard error: z = \(\frac{\hat{p} - p}{SE}\).Using the given numbers, we have:
The sample proportion, \(\hat{p}\), is 42/100 = 0.42.The hypothesized population proportion, p, is 0.35.The sample size, n, is 100.Now we calculate the standard error:
SE = \(\sqrt{\frac{0.35(1-0.35)}{100}}\) = \(\sqrt{\frac{0.35(0.65)}{100}}\) = \(\sqrt{\frac{0.2275}{100}}\) = 0.0477.
Then we calculate the z-score:
z = \(\frac{0.42 - 0.35}{0.0477}\) = \(\frac{0.07}{0.0477}\) = 1.47.
The value of the test statistic for this hypothesis test is 1.47.
Is y=33x proportional or non proportional
Answer:
proportional
Step-by-step explanation:
new car costs $25,000 to build in 2020. The company’s analyst estimates the cost to build will rise 6% every year for the next 10 years. How much will the car cost in 2023?
Answer:
$27,318.18
Step-by-step explanation:
The build cost is multiplied by 1.03 each year. After 3 years, it will be multiplied by 1.03^3, so will be ...
$25,000×1.03^3 ≈ $27,318.18