1. In each of the following pairs, which situation (1) or (2) would pose the largest problems regarding adverse selection?
   
   a. A policy covering accidents for all children attending YMCA camps or (2) A policy covering accidents for college students traveling abroad
   
   b. Basic medical services insurance package offered to students entering college or (2) Basic medical services package offered to professors seeking early retirement

In order to estimate the proportion of students on a particular campus who favor a campus-wide ban on alcohol, a social researcher interviewed a random sample of 100 students from the college population. She found that 36% of the sample favored banning alcohol. (9 points)

            a) Find the mean of the sampling distribution of proportions (µ_p).

            b) Find the standard error of the proportion (σ_p).

            c) Find the estimated standard error of the proportion (s_p).

We want to investigate the average time per day students spend playing video games. We pick a simple random sample of 900 students and record how long they play video games per day. It turns out that the sample average is 2 hours and the SD of the sample is 1.25 hours.

Find the 91% confidence interval for our estimate of the average time per day spent playing video games.

2. Suppose that the researchers are interested in the effect of class size on only female student test scores. They consider using the following method to reconstruct their treatment and control groups: select all female students who have been assigned to small size classes as their new treatment group and select all female students who have been assigned to normal size classes as their new control group. Is this method problematic?

Problem 3

(a) There are 3 male and 3 female students sitting in a row, and they chose their seats randomly.

What is the probably of the event "No two males sit together and no two females sit together"?

(Hint: The gender of the seated students can only be FMFMFM or MFMFMF.)

(b) Compute the probability of randomly drawing ve cards from a deck, and getting two Aces.

(Hint: A deck has 52 cards, and 4 of them are Aces.)

A survey of high school students revealed that the numbers of soft drinks consumed per month was normally distributed with mean 25 and standard deviation 15. A sample of 36 students was selected. What is the probability that the average number of soft drinks consumed per month for the sample was between 28.5 and 30 soft drinks? Write only a number as your answer. Round to 4 decimal places (for example 0.0048). Do not write as a percentage.

A group of students estimated the length of one minute without reference to a watch or​ clock, and the times​ (seconds) are listed below. Use a

0.10

significance level to test the claim that these times are from a population with a mean equal to 60 seconds. Does it appear that students are reasonably good at estimating one​ minute?

Suppose that the average time that students spend online daily is normally distributed with a mean of 244 minutes and st dev of 49 minutes.  Answer the following questions.

1. What is the probability that a randomly picked student spends more than 265 minutes online daily?  Is this unusual, why or why not?

2. If a group of 21 students is randomly selected, what is the probability that their average time spent online is more than 265 minutes?  Is this unusual or not and why?

A survey was conducted at Acadia on attitudes toward the campus alcohol policy against drinking games in residence with 262 randomly selected residence students. In response to the question, “Are you in favour of the drinking games policy?” 25% were in favour. What is the 99% confidence interval to estimate the percentage of all Acadia residence students regarding the drinking game policy? Remember to report your confidence interval in a complete sentence and describe what it means.

Giving a test to a group of students, the grades and gender are summarized below

A B C Total

Male 18 16 6 40

Female 13 19 15 47

Total 31 35 21 87

Let p represent the population proportion of all female students who received a grade of B on this test. Use a 99% confidence interval to estimate p to four decimal places if possible. < p <