Question

The submissions for all hypothesis testing problems must have all six of the hypothesis testing steps.

1. An article in The Wall Street Journal implies that more than half of the all Americans would prefer being given $100 rather than a day off from work. This statement is based on the survey conducted by American Express Incentive Services, in which 593 of 1040 respondents indicated that they would rather have $100 (Carlos Tejeda, “Work Week,” The Wall Street Journal, July 25, 2000, A1).

a.At the 0.05 level of significance, is there evidence based on the survey data that more than half of all Americans would rather have $100 than a day off from work? b.Compute the p-value and interpret its meaning.

Answer 1

a. At the 0.05 level of significance, is there evidence based on the survey data that more than half of all Americans would rather have $100 than a day off from work?

p̂ = 593/1040 = 0.57

The hypothesis being tested is:

H₀: p = 0.5

H_a: p > 0.5

The test statistic, z = (p̂ - p)/√p(1-p)/n

z = (0.57 - 0.5)/√0.5(1-0.5)/1040

z = 4.53

b.Compute the p-value and interpret its meaning.

The p-value for z = 4.53 is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that more than half of all Americans would rather have $100 than a day off from work.