Concept explainers
(a)
To Explain: the type-I error and Type-II error in this setting and give a possible consequence of each.
(a)

Explanation of Solution
Given:
Claim is Proportion is less than 10%
The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis statement is that the population proportion is equal to the value given in the claim. If the null hypothesis is the claim, then the alternative hypothesis statement is the opposite of the null hypothesis.
Type I error is the rejecting the null hypothesis
There is enough convincing proof that the percentage of patients who experience nausea is less than 10%, whereas the percentage of patients who experience nausea is actually 10%.
A possible consequence is that the doctors underestimate the percentage of patients who experience nausea and therefore the side effects are worse then they expect.
Type II error is fails to reject the null hypothesis
There is sufficient convincing evidence that the percentage of patients who experience nausea is less than 10%, while the percentage of patients who experience nausea is actually 10%.
A possible consequence is that the doctors overestimate the percentage of patients who experience nausea and thus the side effects are better then they expect, which could lead to an effective drug not being put on the market (due to the bad side effects).
(b)
To Explain: these data provide convincing proof for the drug manufacturer’s claim.
(b)

Answer to Problem 46E
There is no enough convincing evidence that the drug manufacturer’s claim is false.
Explanation of Solution
Given:
Claim is less than 10%
Formula used:
Calculation:
The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis statement is that the population proportion is equal to the value given in the claim. If the null hypothesis is the claim, then the alternative hypothesis statement is the opposite of the null hypothesis.
Normal: Satisfied, because
are both at least 10.
Since all conditions are satisfied, it is appropriate to use a hypothesis test for the population proportion
The sample proportion is
The test-statistic is
The P-value is the probability of getting the value of the test statistic, or a value more extreme, when the null hypothesis is true. find the P-value using the normal probability table
If the P-value is lesser than the significance level
There is no enough convincing evidence that the drug manufacturer’s claim is false.
Chapter 9 Solutions
PRACTICE OF STATISTICS F/AP EXAM
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