Weekly Earnings of Women According to the Women’s Bureau of the U.S. Department of Labor, the occupation with the highest
1550 | 1355 | 1777 |
1430 | 1570 | 1701 |
2465 | 1655 | 1484 |
1429 | 1829 | 1812 |
1217 | 1501 | 1449 |
a.
To identify: The claim and state
Answer to Problem 8E
The claim is “the median weekly earnings for U.S. women pharmacist is 1603 dollars”.
Null hypothesis:
Alternative hypothesis:
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
b.
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 |
|
Sign | Data | Diff | Sign |
1550 |
|
– | 1484 |
|
– |
1355 |
|
– | 1429 |
|
– |
1777 |
|
+ | 1829 |
|
+ |
1430 |
|
– | 1812 |
|
+ |
1570 |
|
– | 1217 |
|
– |
1701 |
|
+ | 1501 |
|
– |
2465 |
|
+ | 1449 |
|
– |
1655 |
|
+ |
The sample size is,
Critical value:
From table” critical values for sign test” for
The critical value is 3.
c.
To find: the test statistic
Answer to Problem 8E
The test statistic is 6.
Explanation of Solution
Condition:
If
If
Where
Here, the number of
Thus the test statistic is 6.
d.
To decide: Whether to reject or fail to reject the null hypothesis at level of significance
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
If the test statistic is greater than the critical value, then fail to reject the null hypothesis
Conclusion:
The level of significance is,
Here, the test statistic value is greater than the critical value.
That is,
Thus, the decision is “fail to reject the null hypotheses”.
e.
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
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