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Chapter 10: Q. 1 (page 600)

At Rachel鈥檚 11th birthday party, eight girls were timed to see how long (in seconds) they could hold their breath in a

relaxed position. After a two-minute rest, they timed themselves while jumping. The girls thought that the mean difference

between their jumping and relaxed times would be zero. Test their hypothesis.

Short Answer

Expert verified

Since p- the value is greater than 伪=0.05,we cannot reject the hypothesis H0and we can conclude that it is insufficient

evidence to conclude that the average difference is not zero.

Step by step solution

01

Given Information 

We need to test the hypothesis

02

Explanation 

We can take X1-X2to represent the difference between jumping and relaxed time.

We want to test this hypothesis:

H0:渭1=渭2H1:渭1鈮�渭2

In order to test the hypothesis, we are using the Student's test.

03

Simplification 

We need to find the mean and stand deviation of both samples:

渭1=32.375,s1=9.620477渭2=30.625,s2=8.331309

The differences between jumping and relaxed times are given by:

5, 7, 2, 1, - 2, 2, 2 -3

The number of differences is 伪=1.75:

鈭�i-18(di-a)2=75.5

Standard deviation differences are:

8=1n-1鈭�i-18(di-a)2=75.57=3.284

The standard error is: SE=n8=1.161

We can find the value of the test statistic is:

t=渭1-渭2SE=1.507

04

Graphical Presentation 

Using the applet, we get that p-value is 0.17554:

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Most popular questions from this chapter

Mean entry-level salaries for college graduates with mechanical engineering degrees and electrical engineering degrees are believed to be approximately the same. A recruiting office thinks that the mean mechanical engineering salary is actually lower than the mean electrical engineering salary. The recruiting office randomly surveys \(50\) entry level mechanical engineers and \(60\) entry level electrical engineers. Their mean salaries were \(\$46,100\) and \(\$46,700\), respectively. Their standard deviations were \(\$3,450\) and \(\$4,210\), respectively. Conduct a hypothesis test to determine if you agree that the mean

entry-level mechanical engineering salary is lower than the mean entry-level electrical engineering salary.

98. One of the questions in a study of marital satisfaction of dual-career couples was to rate the statement "I'm pleased with the way we divide the responsibilities for childcare." The ratings went from one (strongly agree) to five (strongly disagree). Table 10.26 contains ten of the paired responses for husbands and wives. Conduct a hypothesis test to see if the mean difference in the husband's versus the wife's satisfaction level is negative (meaning that, within the partnership, the husband is happier than the wife).

Wife's Score
2
2
3
3
4
2
1
1
2
4
Husband's
Score
2
2
1
3
2
1
1
1
2
4

102. A recent year was randomly picked from 1985 to the present. In that year, there were 2,051 Hispanic students at Cabrillo College out of a total of 12,328 students. At Lake Tahoe College, there were 321 Hispanic students out of a total of 2,441 students. In general, do you think that the percent of Hispanic students at the two colleges is basically the same or different?

A new windshield treatment claims to repel water more effectively. Ten windshields are tested by simulating rain without

the new treatment. The same windshields are then treated, and the experiment is run again. A hypothesis test is conducted.

Indicate if the hypothesis test is for

a. independent group means, population standard deviations, and/or variances known

b. independent group means, population standard deviations, and/or variances unknown

c. matched or paired samples

d. single mean

e. two proportions

f. single proportion

88. If the level of significance is 0.05, the conclusion is:
a. There is sufficient evidence to conclude that the WDivision teams score fewer goals, on average, than the E teams
b. There is insufficient evidence to conclude that the W Division teams score more goals, on average, than the E teams.
c. There is insufficient evidence to conclude that the W teams score fewer goals, on average, than the E teams score.
d. Unable to determine
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