
Concept explainers
(a)
To test: The significance test on the competitor’s product which provided better UVA and UVB protection.
(a)

Answer to Problem 9UYK
Solution: The results are summarized as
Explanation of Solution
Calculation: The provided data shows that
Here,
The expected number of successes and failures are
The formula of test statistic for z-test is defined as:
Here,
The formula for sample proportion
Here,
Substitute
Therefore, the sample proportion
Use Table A of standard normal probabilities to obtained the probability.
The probability is obtained as
Therefore, the p-value, which is the area in both the tails, is obtained as:
Conclusion: Since
To find: The comparison of results obtained in previous part with the results obtained in Example 8.5.

Answer to Problem 9UYK
Solution: The results obtained in the previous part are the same with the results obtained in Example 8.5.
Explanation of Solution
Calculation: The results obtained in the previous part are summarized as:
The results obtained in Example 8.5 are summarized as:
Though the value of the sample proportion and the test statistic differ, the p-value is same for both the cases. Therefore, the conclusion for both the cases is the same, that is, the sunblock testing data is not significant.
(b)
To find: The 95% confidence interval for the hypothesis that the competitor’s product provides better protection.
(b)

Answer to Problem 9UYK
Solution: The 95% confidence interval for the hypothesis that the competitor’s product provides better protection is
Explanation of Solution
Calculation: The formula for confidence interval in the arrangement of estimate plus or minus the margin of error is:
Here, m is the margin of error, which is defined as:
Here,
The sample proportion is obtained as 0.35 in the previous part. Substitute this proportion in the standard error formula. So,
Therefore, the standard error is obtained as 0.2067. The value of
So, the margin of error is obtained as:
Substitute the values of margin of error and sample proportion in the formula for confidence interval of the arrangement of estimate, plus or minus the margin of error. Therefore, the confidence interval is obtained as:
To explain: The comparison of 95% confidence interval for the competitor’s product providing better protection and the 95% confidence interval for your product providing better protection.

Answer to Problem 9UYK
Solution: The widths of the confidence intervals obtained in both the cases are the same.
Explanation of Solution
The 95% confidence interval for the competitor’s product providing better protection is obtained as
Therefore, these results show that the width of the confidence intervals is the same but only the lower and the upper limit changes.
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Chapter 8 Solutions
EBK INTRODUCTION TO THE PRACTICE OF STA
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