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Improving health A large company's medical director launches a health promotion campaign to encourage employees to exercise more and eat better foods. One measure of the effectiveness of such a program is a drop in blood pressure. The director chooses a random sample of 50employees and compares their blood pressures from physical cams given before the campaign and again a year later. The mean change (after - before) in systolic blood pressure for these 50employees is -6and the standard deviation is 19.8.

(a) Do these data provide convincing evidence of an average decrease in blood pressure among all of the company's employees during this year? Carry out a test at the =0.05significance level.

(b) Can we conclude that the health campaign caused a decrease in blood pressure? Why or why not?

Short Answer

Expert verified

(a) Yes, there is sufficient evidence

(b)No

Step by step solution

01

Part (a) Step 1 : Given Information 

Given in the question that,

Population mean=0

Sample mean(x)=-6

Sample sizen=50

Sample standard deviations=19.8we have to find Do these data provide convincing evidence of an average decrease in blood pressure among all of the company's employees during this year.

02

Part (a) Step 2 :Explanation

The formula to compute the test statistic is:

t=x-sn

using the information, the null and alternative hypothesis are:

H0:=0

H:<0

H0:<0

Using the Ti-83 calculator the output is:

The p-value is less than the significance level. Thus, decision is written as the rejection of the null hypothesis

At 5%significance level, there are sufficient evidence to support the provided claim.

03

 Part (b) Step 1: Given Information

Given in the question that,

Population mean=0

Sample meanx=-6

Sample sizen=50

Sample standard deviations=19.8we have to find Can we conclude that the health campaign caused a decrease in blood pressure.

04

Part (b) Step 2: Explanation 

Because the outcome of an observational study is unaffected, and the case presented is an observational study. As a result, no conclusion can be formed at this time.

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Most popular questions from this chapter

When asked to explain the meaning of the P-value in Exercise 13, a student

says, 鈥淭his means there is only probability 0.01 that the null hypothesis is true.鈥 Explain clearly why the student鈥檚 explanation is wrong.

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Stating hypotheses State the appropriate null and alternative hypotheses in each of the following cases.

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