
Concept explainers
a.
Write the two-tailed decision rule to detect quality control violations using the 5 percent level of significance.
a.

Answer to Problem 23SE
Two-tailed decision rule to detect quality control violations using the 5 percent level of significance is “reject the null hypothesis if
Explanation of Solution
Calculation:
The given information is that, the filling process follows a
The test hypotheses are given below:
Null hypothesis:
That is, the bottles of Galena Spring Water contain an average of 10 ounces.
Alternative hypothesis:
That is, the bottles of Galena Spring Water do not contain an average of 10 ounces.
Critical value:
For two tailed test,
Critical value:
Software procedure:
Step-by-step software procedure to obtain critical value using EXCEL is as follows:
- Open an EXCEL file.
- In cell A1, enter the formula “=NORM.S.INV(0.975)”
- Output using Excel software is given below:
From the output, the critical value of z is
Decision rule for two-tailed test at
If
If
b.
Find the test statistic and make the decision.
b.

Answer to Problem 23SE
The test statistic is 0.78.
The decision is “null hypothesis is not rejected”.
Explanation of Solution
Calculation:
Mean:
Standard deviation:
The formula for standard deviation is,
The value of
10.02 | 0.00001764 |
9.95 | 0.00432964 |
10.11 | 0.00887364 |
10.1 | 0.00708964 |
10.08 | 0.00412164 |
10.04 | 0.00058564 |
10.06 | 0.00195364 |
10.03 | 0.00020164 |
9.98 | 0.00128164 |
10.01 | 0.00003364 |
9.92 | 0.00917764 |
9.89 | 0.01582564 |
The standard deviation is,
The formula for test statistic is,
Where
Substitute
Thus, the test statistic is 0.78.
Conclusion:
Here, the test statistic is less than the critical value. That is,
Therefore, the null hypothesis is not rejected.
c.
Describe the assumptions for given hypotheses tests.
c.

Explanation of Solution
The assumption necessary to validate the given test is the population is normally distributed.
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Chapter 9 Solutions
Applied Statistics in Business and Economics
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