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Chapter 9: Q.67 (page 588)

In the study of older students’ attitudes from Exercise 63, the sample mean SSHA score was 125.7 and the sample standard deviation was 29.8.

(a) Calculate the test statistic.

(b) Find the P-value using Table B. Then obtain a more precise P-value from your calculator.

Short Answer

Expert verified

a. the test statistic is2.409

b. The P-value using Table B is0.0101

Step by step solution

01

Introduction

A test statistic is a statistic utilized in statistical hypothesis testing. A hypothesis test is typically specified as far as a test statistic, considered as a numerical synopsis of an informational collection that decreases the information to one worth that can be utilized to play out the hypothesis test.

02

Explanation Part (a)

The sample size is n = 45

standard deviation s = 29.8

sample mean x-=125.7

Using,

role="math" localid="1652954730678" t=x-−μsn

=125.7−11529.845=2.409

03

Explanation Part (b)

calculating the degree of freedom,

n-1=45-1=44

The p-value is found using,

=Ptc>|0.77|=0.0101

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Most popular questions from this chapter

Haemoglobin is a protein in red blood cells that carries oxygen from the lungs to body tissues. People with less than 12 grams of haemoglobin per deciliter of blood (g/dl) are anaemic. A public health official in Jordan suspects that Jordanian children are at risk of anaemia. He measures a random sample of 50 children.

Is it significant? For students without special preparation, SAT Math scores in recent years have varied Normally with mean μ=518. One hundred students go through a rigorous training program designed to raise their SAT Math scores by improving their mathematics skills. Use your calculator to carry out a test of

H0:μ=518

Hα:μ>518

in each of the following situations.

(a) The students' scores have mean x¯=536.7and standard deviation sx=114. Is this result significant at the5%level?

(b) 'The students' scores have mean x=537.0and standard deviation sx=114. Is this result significant at the 5%level?

(c) When looked at together, what is the intended lesson of (a) and (b)?

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 α=0.05significance level.

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

“I can’t get through my day without coffee” is a common statement from many students. Assumed benefits include keeping students awake during lectures and making them more alert for exams and tests. Students in a statistics class designed an experiment to measure memory retention with and without drinking a cup of coffee one hour before a test. This experiment took place on two different days in the same week (Monday and Wednesday). Ten students were used. Each student received no coffee or one cup of coffee, one hour before the test on a particular day. The test consisted of a series of words flashed on a screen, after which the student had to write down as many of the words as possible. On the other day, each student received a different amount of coffee (none or one cup). (a) One of the researchers suggested that all the subjects in the experiment drink no coffee before Monday’s test and one cup of coffee before Wednesday’s test. Explain to the researcher why this is a bad idea and suggest a better method of deciding when each subject receives the two treatments.

(b) The data from the experiment are provided in the table below. Set up and carry out an appropriate test to determine whether there is convincing evidence that drinking coffee improves memory.

For the job satisfaction study described in Section 9.1, the hypotheses are

H0:μ=0Ha:μisnotequalto0

where μis the mean difference in job satisfaction scores (self-paced machine-paced) in the population of assembly-line workers at the company. Data from a random sample of 18workers gave x⏜=17and sx=60

Calculate the test statistic. Show your work.
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