1. What demographic variables were measured at the nominal level of measurement in the Oh et al. (2014) study? Provide a rationale for your answer. 2. What statistics were calculated to describe body mass index (BMI) in this study? Were these appropriate? Provide a rationale for your answer. 3. Were the distributions of scores for BMI similar for the intervention and control groups? Provide a rationale for your answer. 4. Was there a signifi cant difference in BMI between the intervention and control groups? Provide a rationale for your answer.

We are interested in whether math score (math – a continuous variable) is a significant predictor of science score (science – a continuous variable) using the High School and Beyond (hsb2) data.

State the null and alternative hypotheses and the level of significance you intend to use.

Ho:β=0

H1:β≠0

Alph:0.05

Write the equation for the appropriate test statistic.

t =b/SE(b)

What is your decision rule? Be sure to include the degrees of freedom.

If our t value is greater than the critical value of 1.96 we reject the null hypothesis.

FD= n-2=200-2= 198=1.96

Using SAS, estimate the means, variances and covariances for math and science scores. Copy and paste the relevant SAS output below.

Using the output from (d), calculate by hand the slope. Be sure to show your work.

Using the output from (d), calculate by hand the intercept. Be sure to show your work

Baseball's World Series is a maximum of seven games, with the winner being the first team to win four games. Assume that the Atlanta Braves and the Minnesota Twins are playing in the World Series and that the first two games are to be played in Atlanta, the next three games at the Twins' ballpark, and the last two games, if necessary, back in Atlanta. Taking into account the projected starting pitchers for each game and the home field advantage, the probabilities of Atlanta winning each game are as follows:

a. Set up a spreadsheet simulation model for which whether Atlanta wins or loses each game is a random variable. What is the probability that the Atlanta Braves win the World Series? If required, round your answer to two decimal places.

b. What is the average number of games played regardless of winner? If required, round your answer to one decimal place.

Assume that a sample is used to estimate a population proportion p. Find the 95% confidence interval for a sample of size 380 with 125 successes. Enter your answer as a tri-linear inequality using decimals (not percents) accurate to three decimal places.

___ < p < ____

Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

The director of research and development is testing a new medicine. She wants to know if there is evidence at the 0.1 level that the medicine relieves pain in more than 363 seconds. For a sample of 57 patients, the mean time in which the medicine relieved pain was 367 seconds. Assume the population standard deviation is 24. Find the P-value of the test statistic.

Find the median, the lower half and the upper half of the history 108 test scores 10,16,14,22,21,13,15,14,10,18,19,8,16,12,18,11,9,10,15,10,21,14,18,19,1819,3,25,18,13,1,16,9,14,821,13,14,18,16,5,11,17,14,12,16,18,16,18,17,10,12,19,9,3,15,17

Time spent using e-mail per session is normally distributed,
with m = 9 minutes and s = 2 minutes. If you select a random
sample of 25 sessions,
a. what is the probability that the sample mean is between 8.8 and
9.2 minutes?
b. what is the probability that the sample mean is between 8.5 and
9 minutes?

c. If you select a random sample of 100 sessions, what is the prob-
ability that the sample mean is between 8.8 and 9.2 minutes?

d. Explain the difference in the results of (a) and (c).

When σ is unknown and the sample is of size n ≥ 30, there are two methods for computing confidence intervals for μ.

Method 1: Use the Student's t distribution with d.f. = n − 1.
This is the method used in the text. It is widely employed in statistical studies. Also, most statistical software packages use this method.

Method 2: When n ≥ 30, use the sample standard deviation s as an estimate for σ, and then use the standard normal distribution.
This method is based on the fact that for large samples, s is a fairly good approximation for σ. Also, for large n, the critical values for the Student's t distribution approach those of the standard normal distribution.

Consider a random sample of size n = 31, with sample mean x = 44.4 and sample standard deviation s = 4.7.

(a) Compute 90%, 95%, and 99% confidence intervals for μ using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal.

(b) Compute 90%, 95%, and 99% confidence intervals for μ using Method 2 with the standard normal distribution. Use s as an estimate for σ. Round endpoints to two digits after the decimal.

(c) Compare intervals for the two methods. Would you say that confidence intervals using a Student's t distribution are more conservative in the sense that they tend to be longer than intervals based on the standard normal distribution?

No. The respective intervals based on the t distribution are shorter.Yes. The respective intervals based on the t distribution are shorter.     Yes. The respective intervals based on the t distribution are longer.No. The respective intervals based on the t distribution are longer.

(d) Now consider a sample size of 71. Compute 90%, 95%, and 99% confidence intervals for μ using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal.

(e) Compute 90%, 95%, and 99% confidence intervals for μ using Method 2 with the standard normal distribution. Use s as an estimate for σ. Round endpoints to two digits after the decimal.

(f) Compare intervals for the two methods. Would you say that confidence intervals using a Student's t distribution are more conservative in the sense that they tend to be longer than intervals based on the standard normal distribution?

No. The respective intervals based on the t distribution are shorter.No. The respective intervals based on the t distribution are longer.     Yes. The respective intervals based on the t distribution are longer.Yes. The respective intervals based on the t distribution are shorter.

With increased sample size, do the two methods give respective confidence intervals that are more similar?

As the sample size increases, the difference between the two methods becomes greater.As the sample size increases, the difference between the two methods remains constant.     As the sample size increases, the difference between the two methods is less pronounced.

1. The distribution of body sizes (in g) of wild mosquitoes breeding in the Back Bay Fens was sampled. Fifteen male mosquitoes were weighed, with the following results. Are they larger than the typical male (1.3 g)?

1.60, 1.61, 1.07, 1.34, 1.45, 1.43, 1.16, 2.11, 1.77, 1.08, 1.79, 1.07, 1.59, 2.07, 0.85

1. What is the appropriate test to use for these data? Justify your answer.
2. Test the hypothesis that these mosquitos are significantly larger than the typical male of the species. Let a = 0.05.
3. What is the 95% confidence interval for the mean based on this sample?

The age of Facebook users is normally distributed. The average age of a user on Facebook is 40.5 with a standard deviation of 10. 1. What is the probability that a single randomly selected person that is on Facebook is less than 20 years of​ age? (round to four​ decimals) nothing 2. What is the probability that a sample of 15 Facebook useres is between 30 and 40 years of​ age?

1.  The gestation period (length of pregnancy) for male babies born in New York is normally distributed with a mean of 39.4 weeks and a standard deviation of 2.3 weeks.

(a)  What percent of mothers of male babies are pregnant for less than 35 weeks?

(b)  What percent of mothers of male babies are pregnant for between 35 and 40 weeks?

3. What percent of mothers of male babies are pregnant for more than 40 weeks?
4.   Suppose a sailor had shore leave 46 weeks ago and his wife is delivering a baby today.  What should the sailor say to his wife when he gets home?

Determine the Appropriate Analysis For each of the following scenarios, identify the appropriate analysis.

2. A guidance counselor at a high school wants to be best informed about the universities and colleges that students prefer most frequently. He glances at the institutions attended by last year’s graduates and notes that the three closet colleges appear to have about equal appeal. To test this assumption, he begins asking students who are planning on postsecondary schooling where they will apply. His data are as follows:

The technical institute: 22

The community college: 18

The comprehensive university: 12

Recall the lifetime (in months) of a battery is modeled by a random variable X that has pdf fθ(x)=Kθx1(x>0)where K=ln(1/θ) for an unknown parameter θ∈(0,1) .

Assume instead that we cannot actually observe the lifetime of the batteries. Instead, we only observe if the battery is still working after τ months for some known τ to be chosen later (this is called censored data ).

Let Y1,…,Yn be our observations where Yi=1(Xi>τ) indicates that the i th battery is still working after τ months. Our goal is to estimate θ∈(0,1) (the parameter for the pdf of X ) based on this new data.

The quantity n−−√(θ~−θ) converges in distribution to N(0,σ2~) . Find the asymptotic variance σ2~ . σ2~=

Company A is trying to sell its website to Company B. As part of the sale, Company A claims that the average user of their site stays on the site for 10 minutes. To test this claim Company B collects the times (in minutes) below for a sample of 10 users. Assume normality.

Time 1.6

25.9

7

23.3

7.3

8.8

18.5

8.6

10.8

12

Construct a 95% confidence interval for the true mean time spent on the web site.

a) What is the lower limit of the 95% interval? Give your answer to three decimal places. Enter 0 if your lower limit is less than 0.

b) What is the upper limit of the 95% interval? Give your answer to three decimal places.

c) Based on this data, do you believe the claim made by Company A?

Yes because 10 is not inside the interval.

No because 10 is not inside the interval.

Yes because 10 is inside the interval.

No because 10 is inside the interval.

d) Which of the following assumptions should be checked before constructing the above confidence interval?

the data need to have small variance

the data need to follow a t distribution

the data need to be skewed

the data need to follow a normal distribution

List and explain the t-test assumptions.