Student Debt – Vermont: The average student loan debt of a U.S. college student at the end of 4 years of college is estimated to be about $22,500. You take a random sample of 136 college students in the state of Vermont and find the mean debt is $23,500 with a standard deviation of $2,600. We want to construct a 90% confidence interval for the mean debt for all Vermont college students.

(a) What is the point estimate for the mean debt of all Vermont college students?

(b) What is the critical value of t (denoted t_α/2) for a 90% confidence interval? Use the value from the table or, if using software, round to 3 decimal places.
t_α/2 =

(c) What is the margin of error (E) for a 90% confidence interval? Round your answer to the nearest whole dollar.
E = $

(d) Construct the 90% confidence interval for the mean debt of all Vermont college students. Round your answers to the nearest whole dollar.
< μ <

(e) Based on your answer to (d), are you 90% confident that the mean debt of all Vermont college students is greater than the quoted national average of $22,500 and why?

Yes, because $22,500 is below the lower limit of the confidence interval for Vermont students

.No, because $22,500 is above the lower limit of the confidence interval for Vermont students.   

Yes, because $22,500 is above the lower limit of the confidence interval for Vermont students.

No, because $22,500 is below the lower limit of the confidence interval for Vermont students.

(f) We are never told whether or not the parent population is normally distributed. Why could we use the above method to find the confidence interval?

Because the sample size is greater than 30.

Because the sample size is less than 100.    

Because the margin of error is less than 30.

Because the margin of error is positive.

Please completely answer the below Biostatistic question.

Hurricanes Rita and Katrina caused flooding of large parts of New Orleans, leaving behind large amounts of new sediment. Before the hurricanes, the soils of New Oleans were known to have high concentrations of lead, a dangerous toxin capable of creating potential health hazard. Zaharan et al. (2010) were interested in the human health impacts of the flood and so measured lead concentrations of blood (in ug/dl) of children who lived in 46 different affected areas both before and after the floods. Complete the responses for the following R outputs.

R Output

data: lead$bloodLeadAfter and lead$bloodLeadBefore

t = -6.0538, df = 70.325, p-value = 6.212e-08

alternative hypothesis: true difference in means is not equal to 0

95% confidence interval: -2.563481 -1.293041

sample estimates: mean of x = 3.21087, mean of y = 5.13913

a.) Name the sampling unit and sample size

b.) Name the variable(s) and associated scale(s)

c.) Name the design (one-sample t-test, two-sample t-test, paired t-test)

d.) Is this an appropriate design, given the narrative above? Why or why not?

e.) Name the population parameter of interest, using specific descriptors from the narrative (hint: write what are we estimating in specific terms)

f.) Use the output to write the null hypothesis for the associated t-test (be sure to state it in terms of the population parameter of interest)

g.) Use the confidence interval from the output to write a statement about the set of plausible values for the parameter estimate, and to evaluate the plausibility of the null hypothesis.

h.) Use the null hypothesis to write a statement interpreting the p-value from the output. (Do not use more or less than 0.05.as reasoning)

A nutritionist wants to determine whether people who regularly drink one protein shake per day have different cholesterol levels than people in general. In the general population, cholesterol is normally distributed with u = 190 and o = 30. A person followed the protein shake regimen for two months and his cholesterol is 135. Use the 1% significance level to test the nutritionist's idea. (a) Use the five steps of hypothesis testing.

Expert Please Answer

Population 1:

Population 2:

N= __________

(b) Draw a curve and label the cutoff -2.33, rejection region(s), and sample's score.

f) what is the approximate comparison distribution (the population distribution, or the sampling distribution, why?

g) Is a one tailed or two tailed test appropriate in this situation, and why?

The random variable X follows a Poisson process with the given mean. Assuming mu equals 7, compute the following.

​(a) ​P(4​) ​

(b) ​P(X<4​) ​

(c) ​P(Xgreater than or equals4​) ​

(d) ​P(4less than or equalsXless than or equals8​)

(1 point) The song-length of tunes in the Big Hair playlist of a certain Statistics professors mp3-player vary from song to song. This variation can be modeled by the Normal distribution, with a mean song-length of μ=4.1 minutes and a standard deviation of σ=0.72. Note that a song that has a length of 4.5 minutes is a song that lasts for 4 minutes and 30 seconds.

While listening to a song, the professor decides to shuffle the playlist, which means the mp3-player is to randomly pick a song within this particular playlist, and play this next.

If using/working with z-values, use three decimals.

(a) What is the probability that the next song to be played is between 3.8 and 4.85 minutes long? Answer to four decimals.

(b) What proportion of all the songs in this playlist are longer than 5 minutes? Use four decimals in your answer.

(c) 10% of all the songs in this playlist are at most how long, in minutes? Enter your answer to two decimals, and keep your answer consistent with how the song length has been expressed in this problem.

(d) There are 233 songs in the Big Hair playlist. How many of these would you expect to be longer than 5 minutes in length? Use two decimals in your answer.

(e) From the time he set his mp3-player to shuffle, there has been 16 songs randomly chosen and played in succession. What is the chance that the 16-th song played is the 8-th to be longer than 4.1 minutes? Enter your answer to four decimals.

*If you would like you can use RStudio Statistical Software*

A dairy scientist is testing a new feed additive. She chooses 13 cows at random from a large population. She randomly assigns nold = 8 to the old diet and nnew = 5 to a new diet including the additive. The cows are housed in 13 widely separated pens. After two weeks, she milks each cow and records the milk produced in pounds: Old Diet: 43, 51, 44, 47, 38, 46, 40, 35 New Diet: 47, 75, 85, 100, 58 Let μnew and μold be the population mean milk productions for the new and old diets, respectively. She wishes to test H0 : μnew − μold = 0 against HA : μnew − μold ̸= 0 using α = 0.05.(a) Graph the data as you see fit. Why did you choose the graph(s) that you did and what does it (do they) tell you?(b) Perform the hypothesis test assuming equal population variance. Compute the p-value and make a reject or not reject decision. State your conclusion in the context of the problem. (c) Repeat the previous part, but without the equal variance assumption. (d) Compare the results from part b and c. Which test do you trust more and why? I have answers for (a) and (b) with p-value 0.035 which rejects null hypothesis. Can you help with (c) and (d)? Thank you!

A manufacturing company produces electric insulators. If the insulators break when in​ use, a short circuit is likely to occur. To test the strength of the​ insulators, destructive testing is carried out to determine how much force is required to break the insulators. Force is measured by observing how many pounds must be applied to an insulator before it breaks. The accompanying data are collected from a sample of 30 insulators.

Compute the​ mean, median,​ range, and standard deviation for the force needed to break the insulators.

Force strength of insulators

1880 1727 1658 1614 1637 1780 1520 1696 1590 1664

1869 1766 1637 1664 1637 1777 1554 1755 1764 1869

1827 1743 1786 1685 1810 1750 1683 1810 1657 1740

mean = ____

explain condition under which you would use a nonparametric test

DATA:

Group 1 Group 2

2563 2505

2810 2673

2643 2498

2690 2576

2702 2640

2594 2473

2602 2538

2809 2586

2769 2432

2513 2674

Question:

A hospital wishes to justify the benefits of nutrition programs for pregnant women using birth weight data from newborns. The hospital hopes to show that the mean birth weight for newborns from mothers who complete the program is higher than the birth weight for newborns from mothers who do not complete the program. A group of 20 pregnant women were randomly divided into two groups; the first group received the nutrition program and the second group did not receive the program. The resulting weights (in grams) of the newborn babies from each group are shown below. Assume normality.

a) Assuming equal variance, let μ₁ represent the mean associated with the nutrition program, and let μ₂ represent the mean associated with no nutrition program. What are the proper hypotheses?

b) What is the test statistic? Give your answer to four decimal places.  

c) What is the P-value associated with the test statistic? Give your answer to four decimal places.  

d) What is the appropriate conclusion for the hospital using a 0.05 level of significance?

-Conclude that the mean birth weight with the program is higher than the mean birth weight without the program because the P-value is less than 0.05.

-Fail to reject the claim that the mean birth weight with the program is equal to the mean birth weight without the program because the P-value is greater than 0.05.     

- Reject the claim that the mean birth weight with the program is higher than the mean birth weight without the program because the P-value is less than 0.05.

- Fail to reject the claim that the mean birth weight with the program is equal to the mean birth weight without the program because the P-value is less than 0.05.

Post hoc tests are also known as multiple comparisons.: T or F

Research designs that include more than one factor are called factorial designs.: T or F

The simplest of factorial designs is the two-way analysis of variance (ANOVA).:   T or F

A two-way ANOVA consists of two DVs and one IV.:   T or F

The purpose of factorial ANOVA is to test the mean differences with respect to some IV.: T or F

Suppose W is a standard beta random variable with parameters α=4 and β = 4 which means W has expected value 4/8 and standard deviation 1/6 Suppose X is a normal random variable with mean 9 and standard deviation 8. Answer the following using R code:
a) Calculate the 61st percentile of the distribution of X

b) Calculate the 98th percentile of the distribution of W.

c) What is the expected value of the random variable -8W - 15?

d) What is the standard deviation of the random variable -8W - 15?

e) What is the standard deviation of the random variable ((x-5)/4)+1?

f) If X and W are independent then what is the variance of 6X - 5W + 5?

g) Copy your R script for the above into the text box here.

(a) Suppose that Marks Man is shooting at a target, where the center of the target is at (0, 0) in the
plane. Let fX,Y (x, y) be the joint PDF of his shot. Assume that X and Y are independent random variables,
each distributed as N (0, 1). What is P(X ≥ 0, Y ≥ 0)? (Write your answer as a decimal).

(b) Now suppose Joe Schmo is shooting at the same target, and let fX,Y (x, y) be the joint PDF of his
shot. Assume that X and Y are independent random variables, each distributed as N (−1, 4) (He tends to
miss down and to the left, with a higher variance of his shots.) What is P(X ≥ 1, Y ≥ 0)? (Write your
answer as a decimal).