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 2765 employers responded to the survey, with 964 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.

A button hyperlink to the SALT program that reads: Use SALT.
Do the sample data provide convincing evidence in support of this claim? Test the relevant hypotheses using
= 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 =
P-value

Answer 1

To test the claim that more than one-third of employers have sent an employee home for inappropriate attire, we can set up the following null and alternative hypotheses:

Null hypothesis: p ≤ 1/3

Alternative hypothesis: p > 1/3

where p is the true proportion of all employers who have sent an employee home for inappropriate attire.

We can use the sample proportion, 964/2765 = 0.349, as an estimate of the true proportion p. To test the hypotheses, we can calculate the test statistic z as:

z = (p - 1/3) / sqrt((1/3)*(2/3)/n)

where n is the sample size (2765).

Plugging in the values, we get:

z = (0.349 - 1/3) / sqrt((1/3)*(2/3)/2765) = 4.28

Using a standard normal distribution table or calculator, the P-value for this test is less than 0.0001 (or approximately 0.0000 when rounded to four decimal places), indicating strong evidence against the null hypothesis.

Therefore, we can reject the null hypothesis and conclude that there is convincing evidence to support the claim that more than one-third of employers have sent an employee home for inappropriate attire.