Question

A fund manager wants to know if it is equally likely that the Dow Jones Industrial Average will go up each day of the week. For each day of the week, the fund manager observes the following number of days when the Dow Jones Industrial Average goes up.

Day of the Week Observed
Monday 192
Tuesday 189
Wednesday 202
Thursday 199
Friday 218

Using the p-value approach and α = 0.05, the decision and conclusion are ________.
a. reject the null hypothesis; we can conclude that not all of the proportions are the same
b. do not reject the null hypothesis; we cannot conclude that at least one of the proportions is different from 0.20
c. do not reject the null hypothesis; we can conclude that at least one of the proportions is different from 0.20
d. reject the null hypothesis; we cannot conclude that all of the proportions are not the same

Answer 1

The p-value is compared with the significance level to determine the decision and conclusion of the hypothesis test.

Therefore, the correct answer is: option d). reject the null hypothesis; we cannot conclude that all of the proportions are not the same.

Step-by-step explanation:

The question is asking us to make a decision and draw a conclusion using the p-value approach.

To perform the hypothesis test, we compare the observed frequencies of the Dow Jones Industrial Average going up on each day of the week with the expected frequencies if all proportions were the same.

Calculating the p-value and comparing it with the significance level, we find that the p-value is greater than 0.05.

Therefore, we do not reject the null hypothesis and cannot conclude that all of the proportions are not the same. The correct answer is (d) reject the null hypothesis; we cannot conclude that all of the proportions are not the same.