This assignment mostly parallels HW6 and requires the same data sets.

•   Use the T distribution for all problems involving means. Use t.test for any problems with raw data. Use the.

•   For all hypothesis tests, be sure to state the null and alternative hypotheses using symbols, the value of the test statistic (including df if applicable), the p-value, the decision, and a conclusion in the context of the problem. You do not need to calculate or report critical cut off values.

1.   Identifying H0  and Ha  from Triola. First identify if the given statement is a statement about the null or alternative hypothesis. Then write out the hypotheses.

a)  More than 25% of Internet users pay bills online.

b)  Most households have telephones

c)   The mean weight of women who won Miss America titles is equal to 121 lb.

d)  The percentage of workers who got a job through their college is no more than 2%.

e)  Plain M&M candies have a mean weight that is at least 0.8535 g.

f)   The success rate with surgery is better than the success rate with splinting.

g)  Unsuccessful job applicants are from a population with a greater mean age than the mean age of successful applicants.

Ice Cream Data Set

2.   Test the claim that student’s population mean video score is different than the student’s observed sample mean puzzle score. Use a 5% significance level. Assume the population variances are not equal.

( 1 hypotheses, 1 by-hand calculation, 1 R output, 1 reporting required numbers and how by-hand results compare, 1 decision, 1 interpretation in context for a total of 6 points)

3.   Testing a claim

a)   Test the claim that students with a preference for vanilla ice cream have a population mean puzzle      score that is different than the population mean score for students that prefer chocolate ice cream. Use a 5% significance level. Assume the population variances are not equal. [do this problem using an R   function only, meaning no by-hand calculations are necessary] (1 hypotheses, 1 R output, 1 reporting required numbers and how by-hand results compare, 1 decision, 1 interpretation in context for a total  of 5 points)

b)  Set up a permutation test for the test in part (a) with set.seed(15). You do NOT need to restate   hypotheses, but you should show the histogram of the null distribution with vertical lines marking the boundaries for computation of the p-value. Report the p-value for the permutation test. How does it   compare with the p-value from the test in part (a)? Do you make the same conclusion as in (a),           assuming the same significance level? [Hint:  you need to make a subset of the ice cream data that     only has the flavors vanilla and chocolate]. ( 1 histogram, 1 p-value, and 1 comparison for a total of 3 points)

c)  Do you think the statistical test results from parts (a and b) have practical significance? (1 point)

Birthweight Data Set

4.   Consider birthweights for mothers that are smokers and nonsmokers.

a)  Use R as a calculator to do the “by-hand” calculations (means to show the steps as if you were           solving by hand) to test the claim that the proportion of low birthweight babies is higher for mothers that smoked (use smoked – did not smoke) at the 5% significance level. Show your work in the R      chunk. Assume large sample conditions are met. [be sure to follow all steps for hypothesis testing for this part] (1 hypotheses, 1 by-hand calculations, 1 R output, 1 reporting required numbers and how    by-hand results compare, 1 decision, 1 interpretation in context for a total of 6 points)

b)  Repeat the test in part a) using prop.test in R. You do not need to restate the hypotheses and  other information, as you should get comparable results and the same conclusion. Show that the    square root of the chi-square test statistic from prop.test is equal to the z-score you got in part (a), within rounding error. (2 points)

c)  Do you have confidence in the results of the tests from part a) and part b)? Briefly explain. (1 point)

d)  In the context of this problem, what does it mean if a Type 2 error was committed? Do you think there are any significant consequences if a Type 2 error was made? (2 points)