Of the 93 participants in a drug trial who were given a new experimental

treatment for​ arthritis, 52 showed improvement. Of the 96 participants given a​ placebo, 49 showed improvement. Construct a​ two-way table for these​ data, and then use a 0.05 significance level to test the claim that improvement is independent of whether the participant was given the drug or a placebo.

Complete the following​ two-way table.

improvement no improvement
Drug __ __
Placebo __. __

a. State the null and the alternative hypotheses. Choose the correct answer below.

A. The alternative​ hypothesis: Improvement is independent of whether the participant was given the drug or a placebo. The null​ hypothesis: Improvement and treatment​ (drug or​ placebo) are somehow related.

B. The null​ hypothesis: Improvement is independent of whether the participant was given the drug or a placebo. The alternative​ hypothesis: Improvement and treatment​ (drug or​ placebo) are somehow related.

b. Assuming independence between the two​ variables, find the expected frequency for each cell of the table. Table of expected frequencies

improvement no improvement
Drug ___ ___
Placebo ___. ___
​(Round to the nearest hundredth as​ needed.)

c. Find the value of the chi squaredχ2 test statistic.
chi squaredχ2equals= ___? ​(Round to the nearest thousandth as​ needed.)

d. Use the given significance level to find the chi squaredχ2 critical value. The critical value is ___?. ​(Round to the nearest thousandth as​ needed.)