Question

1) 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 2761 employers responded to the survey, with 974 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.

2) A paper reported that in a representative sample of 288 American teens age 16 to 17, there were 73 who indicated that they had sent a text message while driving. For purposes of this exercise, assume that this sample is a random sample of 16- to 17-year-old Americans. Do these data provide convincing evidence that more than a quarter of Americans age 16 to 17 have sent a text message while driving? Test the appropriate hypotheses using a significance level of 0.01. (Round your test statistic to two decimal places and your P-value to four decimal places.)

z= __

p- value = __

Answer 1

1)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.3333
Alternative Hypothesis, Ha: p > 0.3333

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.3528 - 0.3333)/sqrt(0.3333*(1-0.3333)/2761)
z = 2.17

P-value Approach
P-value = 0.015
As P-value < 0.05, reject the null hypothesis.

2)
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.25
Alternative Hypothesis, Ha: p > 0.25

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.2535 - 0.25)/sqrt(0.25*(1-0.25)/288)
z = 0.14

P-value Approach
P-value = 0.4443
.