Question

In a survey conducted by a website, employers were asked if they had ever sent an employee home because they were dressed inappropriately. A total of 2764 employers responded to the survey, with 968 saying that they had sent an employee home for inappropriate attire. In a press release, the website makes the claim that more than one-third of employers have sent an employee home to change clothes. Do the sample data provide convincing evidence in support of this claim? Test the relevant hypotheses using α = 0.05. For purposes of this exercise, assume that it is reasonable to regard the sample as representative of employers in the United States. (Round your test statistic to two decimal places and your P-value to four decimal places.)

z = 0.9678 Incorrect: Your answer is incorrect.

P-value = 0.0322 Incorrect: Your answer is incorrect.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.3333

H_a : p > 0.3333

= x / n = 968 / 2764 = 0.3502

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.3502 - 0.3333 / [(0.3333 * 0.6667) / 2764]

= 1.887

= 1.89

P(z > 1.89) = 1 - P(z < 1.89) = 0.0294

P-value = 0.0294