Elementary Statistics: A Step By Step Approach
Elementary Statistics: A Step By Step Approach
10th Edition
ISBN: 9781259755330
Author: Allan G. Bluman
Publisher: McGraw-Hill Education
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Chapter 13.2, Problem 8E

Weekly Earnings of Women According to the Women’s Bureau of the U.S. Department of Labor, the occupation with the highest median weekly earnings among women is pharmacist with median weekly earnings of $1603. Based on the weekly earnings listed from a random sample of female pharmacists, can it be concluded that the median is less than $1603? Use α = 0.05.

1550 1355 1777
1430 1570 1701
2465 1655 1484
1429 1829 1812
1217 1501 1449

a.

Expert Solution
Check Mark
To determine

To identify: The claim and state H0 and H1 .

Answer to Problem 8E

The claim is “the median weekly earnings for U.S. women pharmacist is 1603 dollars”.

Null hypothesis:  H0:Median=1,603

Alternative hypothesis: H1:Median<1,603

Explanation of Solution

Given info:

The data shows the number of female pharmacist is 15.

Justification:

Here, the claim is that median weekly earnings for U.S. women pharmacist is lesser than 1603 dollars. This can be written as  Median<1,603 . The complement of the claim is Median=1,603 . In the experiment, the alternative hypothesis indicates the claim.

b.

Expert Solution
Check Mark
To determine

To find: The critical value.

Answer to Problem 8E

The critical value is 3.

Explanation of Solution

Determine sample size n:

Subtract the hypothesized median of 1,603 from the data.

Data Difference=Data1,603 Sign Data Diff Sign
1550 1,5501,603=53 1484 1,4841,603=119
1355 1,3551,603=248 1429 1,4291,603=174
1777 1,7771,603=174 + 1829 1,8291,603=226 +
1430 1,4301,603=173 1812 1,8121,603=209 +
1570 1,5701,603=33 1217 1,2171,603=386
1701 1,7011,603=98 + 1501 1,5011,603=102
2465 2,4651,603=862 + 1449 1,4491,603=154
1655 1,6551,603=52 +

The sample size is,

n=sum of (+) and () signs=6+9=15

Critical value:

From table” critical values for sign test” for n=15 at α=0.05 .

The critical value is 3.

c.

Expert Solution
Check Mark
To determine

To find: the test statistic x

Answer to Problem 8E

The test statistic is 6.

Explanation of Solution

Condition:

If n25, the test statistic for sign test is x .

If n>25 , the test statistic for sign test is z=(x+0.5)0.5nn2

Where x is the smaller number of (+) & () and n is the sample size.

Here, the number of (+) sign in the table is 6 and number of () sign in the table is 9.

Thus the test statistic is 6.

d.

Expert Solution
Check Mark
To determine

To decide: Whether to reject or fail to reject the null hypothesis at level of significance α=0.05 .

Answer to Problem 8E

The decision is “fail to reject the null hypothesis”.

Explanation of Solution

Decision rule:

If the test statistic is less than or equal to the critical value, then reject the null hypothesis H0 .

If the test statistic is greater than the critical value, then fail to reject the null hypothesis H0 .

Conclusion:

The level of significance is, α=0.05 and the critical value is 3.

Here, the test statistic value is greater than the critical value.

That is, Test statistic(=6)>criticalvalue(=3)

Thus, the decision is “fail to reject the null hypotheses”.

e.

Expert Solution
Check Mark
To determine

To interpret: The decision in the context of the original claim.

Answer to Problem 8E

The conclusion is that there is enough evidence to reject the claim that the median weekly earnings for U.S. women pharmacist are less than 1603 dollars.

Explanation of Solution

From the part (d), the null hypothesis is not rejected. Thus, there is enough evidence to reject the claim that the median weekly earnings for U.S. women pharmacist are less than $1,603 at 5% level of significance.

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Chapter 13 Solutions

Elementary Statistics: A Step By Step Approach

Ch. 13.1 - Prob. 10ECh. 13.1 - Prob. 11ECh. 13.1 - Prob. 12ECh. 13.2 - Clean Air An environmentalist suggests that the...Ch. 13.2 - Exercises 132 1. Why is the sign test the simplest...Ch. 13.2 - Prob. 2ECh. 13.2 - Prob. 3ECh. 13.2 - Prob. 4ECh. 13.2 - For Exercises 5 through 20, perform these steps....Ch. 13.2 - Prob. 6ECh. 13.2 - AID: 1825 | 12/01/2018 7. 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A calculator generated...Ch. 13.6 - Prob. 19ECh. 13.6 - Gender of Shoppers Twenty shoppers are in a...Ch. 13.6 - Employee Absences A supervisor records the number...Ch. 13.6 - Skiing Conditions A ski lodge manager observes the...Ch. 13.6 - Prob. 23ECh. 13.6 - Prob. 25ECh. 13.6 - Speeding Tickets A police chief records the gender...Ch. 13.6 - Prob. 27ECh. 13.6 - Prob. 28ECh. 13.6 - Prob. 29ECCh. 13.6 - Prob. 30ECCh. 13.6 - Prob. 31ECCh. 13.6 - Prob. 32ECCh. 13.6 - Prob. 33ECCh. 13 - For Exercises 1 through 13, follow this procedure:...Ch. 13 - Prob. 13.2.2RECh. 13 - Prob. 13.2.3RECh. 13 - Record High Temperatures Shown here are the record...Ch. 13 - Hours Worked by Student Employees Student...Ch. 13 - Prob. 13.4.6RECh. 13 - Prob. 13.4.7RECh. 13 - Prob. 13.5.8RECh. 13 - Prob. 13.5.9RECh. 13 - Prob. 13.6.10RECh. 13 - Prob. 13.6.11RECh. 13 - NBA Scoring Leaders The scoring leaders for the...Ch. 13 - Prob. 13.6.13RECh. 13 - Prob. 13.6.14RECh. 13 - Prob. 1DACh. 13 - Prob. 2DACh. 13 - Prob. 3DACh. 13 - Determine whether each statement is true or false....Ch. 13 - Prob. 2CQCh. 13 - Determine whether each statement is true or false....Ch. 13 - Determine whether each statement is true or false....Ch. 13 - Prob. 5CQCh. 13 - Prob. 6CQCh. 13 - Prob. 7CQCh. 13 - Prob. 8CQCh. 13 - Prob. 9CQCh. 13 - Prob. 10CQCh. 13 - Prob. 11CQCh. 13 - Complete the following statements with the best...Ch. 13 - Prob. 13CQCh. 13 - Prob. 14CQCh. 13 - Prob. 15CQCh. 13 - Prob. 16CQCh. 13 - Textbook Costs Samples of students majoring in law...Ch. 13 - Prob. 18CQCh. 13 - Prob. 19CQCh. 13 - Prob. 20CQCh. 13 - Prob. 21CQCh. 13 - Prob. 22CQCh. 13 - Prob. 23CQCh. 13 - Prob. 24CQCh. 13 - Prob. 25CQCh. 13 - Prob. 26CQ
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