The study mentioned in one example also looked at the severity of fever (rated as mild, moderate or severe) for all subjects who developed one after receiving a flu shot . The following table shows counts for subjects randomized to the group that received the active ingredient of the flu shot and the placebo group that received a sugar injection.

		Severity
Group	Mild	Moderate	Severe
Active	39	12	12
Placebo	19	11	4

The P-value for the chi-squared test equals 0.287. Write the conclusion of the test in context.

One study looked at the severity of fever (rated as mild, moderate or severe) for all subjects who developed one after receiving a flu shot . The following table shows counts for subjects randomized to the group that received the active ingredient of the flu shot and the placebo group that received a sugar injection.

Researchers want to know whether the distribution of the severity of fever is the same in both groups. Formulate appropriate null and alternative hypotheses.

Look back at the previous exercise. The printout from MINITAB reports

Test for difference = 0 (vs not = 0) :

Z = 1 . 46 P- Value = 0.144

Explain how the result of the chi-squared test in (b) in the previous exercise corresponds to this z test result.

Look back at the previous exercise. The printout from MINITAB reports

Test for difference = 0 (vs not = 0) :

Z = 1.46 P-Value = 0.144

Define population proportions $p_1$ and $p_2$ and state the hypotheses for that test.

A Swedish study used 1,360 patients who had suffered a stroke. The study randomly assigned each subject to an aspirin treatment or a placebo treatment. In this study, heart attacks were suffered by 28 of the 684 subjects taking placebo and 18 of the 676 subjects taking aspirin.

Show how to carry out all five steps of the null hypothesis that having a heart attack is not associated with whether one takes placebo or aspirin. (You should get a chi-squared statistic equal to 2.1.) Interpret.

A Swedish study used 1,360 patients who had suffered a stroke. The study randomly assigned each subject to an aspirin treatment or a placebo treatment. In this study, heart attacks were suffer ed by 28 of the 684 subjects taking placebo and 18 of the 676 subjects taking aspirin.

Report the data in the form of a 2 x 2 contingency table.

For alligators caught in two Florida lakes, the following table shows their primary food choice. The four food categories refer to fish, invertebrates (such as snails, insects, or crayfish), birds and reptiles (such as egrets or turtles), and others , including mammals or plants. Is there evidence that primary food choice differs between the two lakes?

The P-value for the chi-squared test is less than 0.001. Write the conclusion of the test in context.

For alligators caught in two Florida lakes, the following table shows their primary food choice. The four food categories refer to fish, invertebrates (such as snails, insects, or crayfish), birds and reptiles (such as egrets or turtles), and others , including mammals or plants. Is there evidence that primary food choice differs between the two lakes?

The $X^2$ value for this table equals 16.79. Based on the df for the corresponding chi-squared distribution, can this be considered large? Why?

For alligators caught in two Florida lakes, the following table shows their primary food choice. The four food categories refer to fish, invertebrates (such as snails, insects, or crayfish), birds and reptiles (such as egrets or turtles), and others , including mammals or plants. Is there evidence that primary food choice differs between the two lakes?

Set up the hypotheses of interest.

For alligators caught in two Florida lakes, the following table shows their primary food choice. The four food categories refer to fish, invertebrates (such as snails, insects, or crayfish), birds and reptiles (such as egrets or turtles), and others, including mammals or plants. Is there evidence that primary food choice differs between the two lakes?

Find the conditional sample distributions of primary food choice in lakes Hancock and Trafford.

In 2010 the GSS asked whether a subject was willing to accept cuts in the standard of living to help the environment (GRNSOL), with categories (vw = very willing, fw = fairly willing, nwu = neither willing nor unwilling, nvw = not very willing, nw = not at all willing). When this was cross-tabulated with whether the respondent is currently in school or has retired (WORKSTAT), as shown below, $X^2$ = 9.56.

What conclusion would you make , using a significance level of

(i) 0.05 and

(ii) 0.025? State your conclusion in the context of this study.

In 2010 the GSS asked whether a subject was willing to accept cuts in the standard of living to help the environment (GRNSOL), with categories (vw = very willing, fw = fairly willing, nwu = neither willing nor unwilling, nvw = not very willing, nw = not at all willing). When this was cross-tabulated with whether the respondent is currently in school or has retired (WORKSTAT), as shown below, $X^2$ = 9.56.

Is the P-value less than

(i) 0.05?

(ii) 0.025? Explain.

In 2010 the GSS asked whether a subject was willing to accept cuts in the standard of living to help the environment (GRNSOL), with categories (vw = very willing, fw = fairly willing, nwu = neither willing nor unwilling, nvw = not very willing, nw = not at all willing). When this was cross-tabulated with whether the respondent is currently in school or has retired (WORKSTAT), as shown below, $X^2$ = 9.56.

Report r and c and the df value on which $X^2$ is based.

In 2010 the GSS asked whether a subject was willing to accept cuts in the standard of living to help the environment (GRNSOL), with categories (vw = very willing, fw = fairly willing, nwu = neither willing nor unwilling, nvw = not very willing, nw = not at all willing). When this was cross-tabulated with whether the respondent is currently in school or has retired (WORKSTAT), as shown below, $X^2$ = 9.56

What are the hypotheses for the test to which $X^2$ refers?