1. Pedro thinks that he has a special relationship with the number 4. In particular, Pedro thinks that he would roll a 4 with a fair 6-sided die more often than you'd expect by chance alone. Supposepis the true proportion of the time Pedro will roll a 4.

(a) State the null and alternative hypotheses for testing Pedro's claim. (Type the symbol "p" for the population proportion, whichever symbols you need of "<", ">", "=", "not =" and express any values as a fraction e.g.p = 1/3)

H0=

Ha=

(b) Now suppose Pedro makes n = 38 rolls, and a 4 comes up 8 times out of the 38 rolls. Determine the P-value of the test:

P-value =

(c) Answer the question: Does this sample provide evidence at the 5 percent level that Pedro rolls a 4 more often than you'd expect?

(Type: Yes or No)

2. An Office of Admission document claims that 54.1% of UVA undergraduates are female. To test this claim, a random sample of 220 UVA undergraduates was selected. In this sample, 52.7% were female. Is there sufficient evidence to conclude that the document's claim is false? Carry out a hypothesis test at a 1% significance level.

A. The value of the standardized test statistic:

Note:For the next part, your answer should use interval notation. An answer of the form(,a)is expressed (-infty, a), an answer of the form(b,)is expressed (b, infty), and an answer of the form(,a)(b,)is expressed (-infty, a)U(b, infty).

B. The rejection region for the standardized test statistic:

C. The p-value is =

D. Your decision for the hypothesis test:

A.Do Not RejectH1.

B.RejectH1.

C.RejectH0.

D.Do Not RejectH0.

3. In order to compare the means of two populations, independent random samples of200observations are selected from each population, with the following results:

Sample 1

X1 bar = 5

S1 = 180

Sample 2

X2 bar = 4

S2 = 130

(a)Use a97% confidence interval to estimate the difference between the population means(12).

(1 2)

(b)Test the null hypothesis:H0: (12)=0versus the alternative hypothesis:Ha: (12). Usingalpha=0.03, give the following:

(i)the test statisticz =

(ii)the positive criticalzscore

(iii)the negative criticalzscore

The final conclusion is

We can reject the null hypothesis(12)=0in favor of the alternative(12)0.

There is not sufficient evidence to reject the null hypothesis(12)=0.

(c)Test the null hypothesis:H0: (12)=28versus the alternative hypothesis:Ha: (12)28. Usingalpha=0.03, give the following:

(i)the test statisticz =

(ii)the positive criticalzscore

(iii)the negative criticalzscore

The final conclusion is:

We can reject the null hypothesis(12)=28in favor of the alternative(12)28.

Thereis not sufficient evidence to reject the null hypothesis(12)=28.