Logic Problem

In spite of what may seem obvious, medical research has shown that being cold is not related to catching a cold. Imagine that in one such study, 40 subjects were exposed to cold viruses. Then half of the subjects were randomly assigned to remain in a cold room for several hours, and the other half remain in a room kept at ordinary room temperature. At the end of the experiment, the numbers of subjects who catch a cold are as shown in the following table:
cold room normal temperature room Total
caught cold 14 12
no cold 6 8
Total
a. What is the null hypothesis? Being cold is not related to catching a cold.

b. test the null hypothesis at the .05 level. What is the value of the critical value? What is the value of the test statistic (show work)? What is your conclusion?

c. given your decision, which type of error (type I or II) could you be making ?

Question

A famous logic problem has four possible answers (A, B, C, and D). Extensive study has demonstrated that 40% of the population chooses the correct answer A, 26% choose B, 20% choose C, and 14% choose D. A new study has been conducted with 50 subjects to determine whether presenting the problem in concrete terms changes the way subjects solve the problem. In the new study, 24 subjects choose A, 8 subjects choose B, 16 subjects choose C, and only 2 subjects choose D.

a. State the null and alternative hypotheses

b. Calculate the appropriate test statistic .

c. How many degrees of freedom are there for this test statistic?

d. What is the critical value for alpha = .05 ?

e. State your conclusions in terms of the original research question