2. A random sample of 29 employees of a large company has their systolic blood pressure checked. Summary statistics are provided in the table below. Assume that the systolic blood pressure of all U.S. adults follows a normal distribution with a mean of 122 mm Hg and a standard deviation of 20 mm Hg.
(a) Approximately what percent of all U.S. adults have systolic blood pressure greater than 142 mm Hg?
(b) Describe the distribution of systolic blood pressure for the 29 employees of this company that was sampled.
(c) The company CEO wants to know if the mean systolic blood pressure of employees at her company is higher than the national average. State the hypotheses for testing this concern.
(d) The conditions for the hypothesis test in part (c) were satisfied. The hypothesis test resulted in a t-score of 5.495 and a p-value of 3.591 × 10−6. Interpret the p-value in the context of this hypothesis test. What would this p-value lead you to conclude?
(e) Explain in context what it would mean to make a type II error for the hypothesis test in part (c).
In addition to recording the systolic blood pressure of the 29 employees at the company, their ages were also recorded. A linear regression model was fit to these data. Graphical and numerical summaries of this analysis are given below. Use this information to answer the questions that follow. (Image is attached below)
(f) Interpret the slope of the regression line in this context.
(g) Comment on the strength, direction, and form of the relationship between age and systolic blood pressure.
Answers
Answer:
Step-by-step explanation:
Hello!
The variable of interest is
X: Systolic blood pressure of a U.S. adult. (mmHg)
X~N(μ;σ²)
μ= 122 mmHg
σ= 20 mmHg
For all calculations you have to work under the standard normal distribution, because it is tabulated. It is easier and faster to standardize or "translate" all values of X into values of Z and look for the corresponding probabilities in the table than to manually calculate them using the density function of the normal distribution.
The standard normal distribution is derived from the normal distribution. Considering a random variable X with normal distribution, mean μ and variance δ², the variable Z =(X-μ)/δ ~N(0;1) is determined.
Any value of any random variable X with normal distribution can be "converted" by subtracting the variable from its mean and dividing it by its standard deviation.
Since the distribution is centered in zero, there are two entries for its table, the left entry shows the cumulated probabilities corresponding to negative values of Z: P(Z≤z)=α and the right entry show the cumulated probabilities corresponding to positive values of Z: P(Z≤z)= 1 - α
a)
You need to calculate the percentage/ proportion of U.S. adults that have a systolic pressure greater than 142 mmHg, symbolically:
P(X>142) = 1 - P(X≤142)
To standardize this value od the variable you have to do the following calculation:
Z =(X-μ)/δ= (142-122)/20= 1
Now you look in the right entry for the cumulative probability until z= 1.00
(Remember, the first column of the table shows you the integer and first digit, the first row of the table shows you the second integer of the z value)
P(Z≤1)= 0.84134
Now you calculate the asked value:
P(X>142) = 1 - P(X≤142)= 1 - P(Z≤1)= 1 - 0.84134= 0.15866
b)
The sample mean is derived from a random variable with a normal distribution it shares that distribution with the exception that its variance is directly affected by the sample size:
X[bar]~N(μ;σ²/n)
μ= 122 mmHg
σ/√n= 20/√29= 3.71 mmHg
c)
The claim is that the mean systolic pressure of the employees is higher than the national average, symbolically μ> 122
The statistical hypotheses are:
H₀: μ≤ 122
H₁: μ> 122
d)
t= 5.495 p-value: 0.000003591
In this example the test statistic depends on the mean and the p-value is 3.591*10⁻⁶. This value indicates that 0.0003591% of the samples with size n=29 taken from a population with mean 122 mmHg, will produce a mean that provides evidence as (or stronger) than the current sample that μ is not at most 122 mmHg.
e)
The type II error is the scenario when you fail to reject the null hypothesis when the hypothesis is false. In this case, it is to fail to reject that the average systolic pressure of the company's employees is at most as the national average.
f)
The variable "X: Age of an employee" was recorded and linear regression of the systolic blood pressure as a function of the employee's ages estimated.
^Y= 97.0771 + 0.9493Xi
0.9493mmHg/years is the modification of the estimated average systolic blood pressure of the company's employees when their age increases one year.
g)
To determine the type of linear regression between the two variables, you have to analyze the slope of the equation:
As you can see in the graphic, the slope of the regression is positive, which means there is a positive regression between the systolic pressure and the age of the employees. I.e. each time the age of the employee increases, his systolic pressure also increases.
To determine the strength of the regression between these two variables you have to analyze the coefficient of determination R²:
The coefficient of determination gives you an idea of how much of the variability of the dependent variable (Y) is due to the explanatory variables under the estimated regression. It takes values between 0 to 1 or 0 to 100% if expressed in percentage. The closer the coefficient is to zero, the weaker the relationship between these two variables.
The closer the coefficient is to 100%, the stronger the relationship between these two variables.
R²= 0.712
71.2% of the variability of the systolic pressure is explained by the age fo the employees under this estimated model ^Y= 97.0771 + 0.9493Xi
The relationship between these variables is strong enough to consider the regression.
I hope this helps!
Related Questions
What is the perimeter, in feet, of a square whose area is 9 square feet
Answers
Answer:
12 feet.
Step-by-step explanation:
Note that by definition of a square, all side measurements are the same (as all sides are congruent).
You can solve the area of square by using the following equation:
A (square) = s²
A (square) = side x side.
Plug in 9 for A in the equation:
9 = s²
Isolate the variable, s. Root both sides:
√9 = √s²
s = √9 = √(3 * 3) = 3
One side of the square is 3 feet.
Next, solve for the perimeter. A square has 4 congruent sides, so multiply 3 with 4:
3 x 4 = 12 feet
12 feet is your answer.
~
10 = - 9 - x
Show me all the steps
Answers
Step-by-step explanation:
10= - 9 - X
- x - 9 = 10
-× = 10 + 19
-× =19
× = -19
Subtract the following military times 2330 - 0540
Answers
The final result is 17 hours and 50 minutes, or in military time format, 1750.
To subtract the military times 2330 and 0540, we can approach it as a regular subtraction problem, but we need to borrow from the hour when the minutes in the subtrahend (0540) are larger than the minutes in the minuend (2330). Since military time is on a 24-hour clock, we treat 2330 as 23 hours and 30 minutes, and 0540 as 5 hours and 40 minutes.
Step 1: Since we cannot subtract 40 minutes from 30 minutes, we need to borrow 1 hour from the 23 hours, converting it to 22 hours and 90 minutes.
Step 2: Now we subtract the minutes: 90 minutes - 40 minutes = 50 minutes.
Step 3: Then we subtract the hours: 22 hours - 5 hours = 17 hours.
So, the final result is 17 hours and 50 minutes, or in military time format, 1750.
-4.0 -y=24
Complete the missing value in the solution to the equation.
8)
Answers
Answer:
y=-28
Step-by-step explanation:
add 4 to both sides which gets you -y =28. Then you have to move the negative sign to the other side because y can't end with a negative
Haala buys 13 identical shirts and 22 identical ties for £363.01
The cost of a shirt is £15.35
Find the cost of a tie.
Answers
Answer:
£7.43
Step-by-step explanation:
The total cost is ...
13s +22t = 363.01
13(15.35) +22t = 363.01 . . . . fill in the cost of a shirt
22t = 163.46 . . . . . . . . . . . . . subtract 199.55
t = 7.43 . . . . . . . . . . . divide by 22
The cost of a tie is £7.43.
What value of y makes the equation true. y+2.9=11
Answers
Answer:
y = 8.1
Step-by-step explanation:
y+2.9=11
Subtract 2.9 from each side
y+2.9-2.9 = 11-2.9
y =8.1
Find the circumference of circle L. Write your answer as a decimal, rounded to the nearest hundredth.
please show work
Answers
find the leght of the arch for one degree by doing
2.25 ÷ 114°
u will get
0.0197368421 ft every 1°
and since a full circumference is equal to 360°, just do this:
0.0197368421 ft × 360° = 7.10526315789 ft
ROUND IT OFFFFFF
u get 7.105 ft
VOILA
14. Find the height of a cylinder if the surface area is 408.41 square inches and the radius is 5
inches.
Answers
Final answer:
To find the height of a cylinder with a given surface area and radius, use the formula for the surface area of a cylinder. In this case, the height is approximately 4 inches.
Explanation:
Surface Area of a Cylinder Formula: S = 2πrh + 2πr²
Given: surface area = 408.41 sq in, radius = 5 in
Plug in the values: 408.41 = 2π(5)h + 2π(5)²
Solve for height: h = (408.41 - 50π) / 10π ≈ 4 in
Therefore, the height of the cylinder is approximately 4 inches.
What is the circumference of a circle with a radius of 56 feet?
feet
(Use 3.14 for Pi.)
Answers
Answer:
351.68
Step-by-step explanation:
c = 2πr
c = 2(3.14)(56)
c = 6.28(56)
c = 351.68
Answer:
Step-by-step explanation:
Which function's graph has axis of symmetry x = 2?
y = 3x² + 12x+6
y = 3x2 - 6x+12
y=-3x2 - 12x+6
y=-3x2 + 12x+6
Answers
Answer:
y=-3x2 - 12x+6 , x = -(-12)/2*3 = 2 this one has axis of symmetry x = 2
Step-by-step explanation:
y = 3x² + 12x+6 : x = -12/6 = -2
y = 3x2 - 6x+12 , x = -(-6)/2*3 = -1
y=-3x2 - 12x+6 , x = -(-12)/2*3 = 2 this one
y=-3x2 + 12x+6 , x = -12/2*3 = -2
I don’t know this..I need help
Answers
Answer:
26
Step-by-step explanation:
To find the area of a triangle, you simply need to multiply the base by the height and divide by 2. In this case, 13*4/2=26 square centimeters. Hope this helps!
Gary used 8 gallons of gas to travel 176 miles. How many miles can Gary travel on 1 gallon of gas
Answers
Answer: Gary can travel 22 miles on 1 gallon gas.
Step-by-step explanation:
176/8 = 22
Which would be the most appropriate subject line for
the e-mail with this claim?
Claim: Cell phones should be allowed in schools
because banning them is no longer universally
accepted as the best policy.
YOUR POLICY IS TERRIBLE
Cell phones as an educational tool
Help! Students are at a disadvantage!
You should know that.
Answers
Answer:
B ✔️
Step-by-step explanation:
"Cell phones as an educational tool"
A roller coaster travels 80 ft of track from the loading zone before reaching its peak. The horizontal distance between the loading zone and the base of the peak is 50 ft. At what angle, to the nearest degree, is the roller coaster rising?
Answers
Answer:
the answer is answer b, or 30.83ft
Step-by-step explanation:
A new alloy is made by mixing 72 grams of iron with 9 grams of zinc. How many grams of iron are required to make the alloy when combined with 144 grams of zinc?
A) 992 grams
B) 1,152 grams
C) 1,226 grams
D) 1,445 grams
Answers
Answer:
B) 1,152 grams
Step-by-step explanation:
On a certain portion of an experiment, a statistical test result yielded a p-value of 0.21. What can you conclude? 2(0.21) = 0.42 < 0.5; the test is not statistically significant. If the null hypothesis is true, one could expect to get a test statistic at least as extreme as that observed 21% of the time, so the test is not statistically significant. 0.21 > 0.05; the test is statistically significant. If the null hypothesis is true, one could expect to get a test statistic at least as extreme as that observed 79% of the time, so the test is not statistically significant. p = 1 - 0.21 = 0.79 > 0.05; the test is statistically significant.
Answers
Answer: correct: B. If the null hypothesis is true, one could expect to get a test statistic at least as extreme as that observed 21% of the time, so the test is not statistically significant.
Step-by-step explanation:
the test of the statistical p helps us to find the probability that a statistical value occurs in the null hypothesis, in the exercise we obtain a value of p of 0.21, we assume that for it to have statistical significance the value must be less than 0.05 which is constant, if this result is higher it indicates that there is no statistically significant evidence
Find the length of the arc. Round to the nearest tenth.
Answers
Answer:28.8 m
Step-by-step explanation:
length of arc=theta/360 x 2 x π x radius
Length of arc=150/360 x 2 x3.14x11
length of arc=(150x2x3.14x11) ➗ 360
Length of arc =10362 ➗ 360
Length of arc =28.8
x 2 + 13x + 40 = 0
solving quadratic
Answers
Answer: x=-5 or x=-8
Step-by-step explanation:
x^2+13x+40=0
x^2 + 8x + 5x +40=0
x(x+8)+5(x+8)=0
(x+5)(x+8)=0
x+5=0 or x+8=0
x=-5 or x=-8
If liam ate 4 apples out of a tree of 100 apples how many does he have left?
Answers
Answer:
96 apples
Step-by-step explanation:
100-4=96
Answer:
96
Step-by-step explanation:
Bruh just subtract 4 from 100 like seriously XD
According to the US Bureau of labor statistics, 7% of US female workers between 16 and 24 years old are paid at the minimum wage or less. A state politician wants to verify this statement for his state. He uses a sample of 500 female workers and finds 42 are paid at the minimum wage or less. Use a 5% significance level to test to test whether that state differs from the nation.
State clearly the null and the alternative hypothesis, the test statistic, the decision rule and the conclusion.
Answers
Answer:
The Null Hypothesis is [tex]H_o:k_o = 0.07[/tex]
The alternative hypothesis is [tex]H_a :k_o \ne 0.07[/tex]
Decision rule
If the test staistics is greater than the critical value of significance level then [tex]H_o[/tex] is accepted else [tex]H_o[/tex] is rejected
With the above in mind
The critical value of the significance level which is obtained from the table is
[tex]t_{0.05} = 1.645[/tex]
Now since the critical value of significance level is greater than the test staistics then the null hypothesis will be rejected
Conclusion
The information is not enough to back the claim that state differs from the nation
Step-by-step explanation:
From the question we are told that
The percentage of US female workers paid at the minimum wage or less is [tex]k_o =[/tex] 7% = 0.07
The sample size is [tex]n = 500[/tex]
The number paid minimum wage or less is x = 42
The significance level is [tex]\alpha =[/tex]5% = 0.05
Now the probability of getting a US female workers paid at the minimum wage or less is mathematically represented as
[tex]\= k = \frac{x}{n}[/tex]
substituting value
[tex]\= k = \frac{42}{500}[/tex]
[tex]\= k = 0.084[/tex]
The Null Hypothesis is [tex]H_o:k_o = 0.07[/tex]
The alternative hypothesis is [tex]H_a :k_o \ne 0.07[/tex]
Generally the test statistics is mathematically evaluated as
[tex]z = \frac{\= k - k_o}{\sqrt{\frac{k_o(1-k_o)}{n} } }[/tex]
substituting value
[tex]z = \frac{0.084 - 0.07}{\sqrt{\frac{0.07 (1-0.07)}{500} } }[/tex]
[tex]z = 1.23[/tex]
Now the Decision rule is stated as
If the test staistics is greater than the critical value of significance level then [tex]H_o[/tex] is accepted else [tex]H_o[/tex] is rejected
With the above in mind
The critical value of the significance level which is obtained from the table is
[tex]t_{0.05} = 1.645[/tex]
Now since the critical value of significance level is greater than the test staistics then the null hypothesis will be rejected
So the conclusion will be
The information is not enough to back the claim that state differs from the nation
what is the circumference of a circle with a diameter of 5?
Answers
Answer:
C≈15.71cm
Step-by-step explanation:
C=2πr
d=2r
C=πd=π·5≈15.70796cm
A flock of broiler chickens has a mean weight gain of 700 g between ages 5 and 9 weeks, and the narrow-sense heritability of weight gain in this flock is 0.80. Selection for increased weight gain is carried out for 5 consecutive generations, and in each generation the average of the parents is 50 g greater than the average of the population from which the parents were chosen.
Assuming that the heritability remains constant at 0.80, what is the expected mean weight gain after the 5 generations of selection?
Answers
The expected mean weight gain of the broiler chickens after 5 generations of selection is 900 grams.
Explanation:The expected mean weight gain of the broiler chickens can be calculated using the equation:
Σ = µ + (h^2 * S * t)
where µ is the initial population mean, h^2 is the heritability, S is the selection differential, and t is the number of generations.
From the question:
µ = 700gh^2 = 0.80S = 50gt = 5 generationsSubstituting these values into the equation gives:
Σ = 700g + (0.80 * 50g * 5) = 700g + 200g = 900g
So, the expected mean weight gain after 5 generations of selection is 900 grams.
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After 5 generations of selection with a heritability of 0.80 and a selection differential of 50 g, the expected mean weight gain for the flock is 900 g.
To determine the expected mean weight gain after 5 generations, we use the breeder's equation, which is R = h²S, where R is the response to selection, h² is the narrow-sense heritability, and S is the selection differential.
The narrow-sense heritability h² is given as 0.80 and the selection differential S is 50 g. Therefore, the response to selection for one generation is:⇒ R = h² x S
⇒ 0.80 x 50 g = 40 g
After 5 generations, the total expected gain can be calculated by multiplying the response by the number of generations:⇒ Total gain = R x 5
⇒ 40g/generations x 5 generations = 200 g
Starting with the initial mean weight gain of 700 g, we add the total gain:⇒ Expected mean weight gain after 5 generations = 700 g + 200 g
= 900 g
Thus, the expected mean weight gain after 5 generations of selection is 900 g.
Find the area and perimeter of the given rectangle.
Answers
Answer:
Area: 48 sq. units
Perim: 28 units
Step-by-step explanation:
The distance between (-4, 3) and (-4,-3) is 6. The distance between (-4,-3) and (4,-3) is 8. So, 6 x 8 is 48, and that is the area.
6, 6, 8, and 8 are the lengths, so add those up to find the perimeter and you get 28.
F(x)=4x-1 and G(x) =x2+7 what is G(F(x)
Answers
Answer:
The answer is 16x^2-8x+8
The answer is c
Step-by-step explanation:
g(x)=x2+7
g(f)(x)= (4x-1)2+7
= (4x-1) (4x-1) + 7
= 16x2 -4x -4x + 1 +7
= 16x 2 -8x +8x
Recall that the primes fall into three categories: Let Pi be the set of
primes congruent to 1 (mod 4) and P3 be the set of primes congruent to
3 (mod 4). We know that
{primes} = {2} UP, UP3.
We have previously proved that P3 is infinite. This problem completes
the story and proves that P1 is infinite. You can do this by following these
steps:
A) Fix n > 1 and define N = (n!)2 + 1. Let p be the smallest prime divisor
of N. Show p>n.
B) If p is as in part (a), show that p ⌘ 1 (mod 4). (To get started, note
that (n!)2 ⌘ 1(mod p), raise both sides to the power p1 2 and go from
there. You will need Fermat’s Theorem)
C) Produce an infinite increasing sequence of primes in P1, showing P1
is infinite.
Answers
Answer:
Check the explanation
Step-by-step explanation:
(a)Let p be the smallest prime divisor of (n!)^2+1 if p<=n then p|n! Hence p can not divide (n!)^2+1. Hence p>n
(b) (n!)^2=-1 mod p now by format theorem (n!)^(p-1)= 1 mod p ( as p doesn't divide (n!)^2)
Hence (-1)^(p-1)/2= 1 mod p hence [ as p-1/2 is an integer] and hence( p-1)/2 is even number hence p is of the form 4k+1
(C) now let p be the largest prime of the form 4k+1 consider x= (p!)^2+1 . Let q be the smallest prime dividing x . By the previous exercises q> p and q is also of the form 4k+1 hence contradiction. Hence P_1 is infinite
Anthony is informed that there is a 10% chance that he will be hired by the prestigious Acme corporation. He believes that, given his outstanding skill as a golfer, once he is hired there is an 80% chance that he will earn a spot on the celebrated Acme Corporation golf team. Given this information we can estimate that the likelihood that Anthony will soon be playing on the Acme golf team to be:
Answers
Answer:
8% probability that Anthony will soon be playing on the Acme golf team
Step-by-step explanation:
We have these following probabilities:
10% probability that he is hired by the corporation.
If he is hired by the corporation, an 80% probability that he will earn a spot on the golf team.
Given this information we can estimate that the likelihood that Anthony will soon be playing on the Acme golf team to be:
80% of 10%
So
P = 0.8*0.1 = 0.08
8% probability that Anthony will soon be playing on the Acme golf team
which word describes the four angels formed by the intersection of two perpendicular lines
Answers
The word that describes the four angles formed by the intersection of two perpendicular lines is "right angles" because they each measure 90 degrees and create an L-shaped corner.
The four angles formed by the intersection of two perpendicular lines are often described as "right angles." A right angle measures exactly 90 degrees, and it is the angle at which two lines meet and form a perfect L shape.
Right angles are a fundamental concept in geometry and have many practical applications in everyday life. They are essential in fields such as architecture, engineering, and mathematics. Right angles are known for their symmetry and balance, making them a crucial element in various geometric shapes and constructions.
In summary, the word that describes the four angles formed by the intersection of two perpendicular lines is "right angles" due to their characteristic 90-degree measurement and significance in geometry.
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Complete question below :
What word describes the four angles formed by the intersection of two perpendicular lines?
The volume of a CONE-shaped hole is 75pi ft cubed. If the hole is 9 feet deep, what is the radius of the hole?
(1 Point)
Answers
Answer:
The radius of hole is 5 feet
Step-by-step explanation:
Depth of conical hole = 9 feet
Let the radius of hole be r
Volume of conical hole =[tex]\frac{1}{3} \pi r^2 h[/tex]
So, Volume of conical hole =[tex]\frac{1}{3} \pi \times r^2 \times 9[/tex]
We are given that volume of a CONE-shaped hole is 75pi ft cubed.
So,[tex]\frac{1}{3} \pi \times r^2 \times 9=75 \pi[/tex]
[tex]\frac{1}{3} \times r^2 \times 9=75[/tex]
[tex]r^2=\frac{75 \times 3}{9}[/tex]
[tex]r=\sqrt{\frac{75 \times 3}{9}}[/tex]
r=5
Hence The radius of hole is 5 feet
The two-way table below describes the practice habits of members of the school band and choir.
Practice Habits of School Musicians
Less than
30 Minutes per Day
38
At Least
30 Minutes per Da
26
12
Band Students
Choir Students
Which statement best describes the relationship between the two variables?
O
O
There is an association because the relative frequencies by row are different.
There is an association because the relative frequencies by row are similar.
There is no association because the relative frequencies by row are different.
There is no association because the relative frequencies by row are similar.
O
Mark this and return
Save and Exit
Next
Answers
Answer:
D.
Step-by-step explanation:
i took the quiz
A college official conducted a survey to estimate the proportion of students currently living in dormitories about their preference for single rooms, double rooms, or multiple (more than two people) rooms in the dormitories on campus. Which of the following does not a ect the college official's ability to generalize the survey results to all dormitory students?(a) Five thousand students live in dormitories on campus. A simple randomsample of only 500 were sent the survey.(b) The survey was sent only to first year students.(c) Of the 500 students who were sent the survey, only 160 responded.(d) All of the above present a problem for generalizing the results.
Answers
Answer:
b
Step-by-step explanation:
all the options reflect the college's official's ability ot generalize the survey results except b. Option b represents a particular group of the total population.
The ability to generalize survey results is compromised when the survey is biased, the sample size is inadequate relative to the population, or the response rate is low. Each of the listed issues affects the generalizability of the survey outcome, with specific concerns in terms of sample representativeness and potential biases.
Explanation:The question concerns the ability to generalize survey results to a larger population of dormitory students. Options a, b, and c each presents issues related to sample representativeness and survey methodology, which can affect the college official's ability to generalize findings.
Option a suggests that the sample may be too small relative to the total population. However, a random sample of 500 can theoretically represent 5,000 students well if selected appropriately. Option b indicates a selection bias because only first-year students were surveyed, which does not reflect the entirety of dormitory residents.
Option c points to a low response rate, which can result in nonresponse bias if the 160 respondents have different preferences than those who did not respond.