Concept explainers
(a)
To Explain: that there is convincing at the
(a)
Answer to Problem 74E
There is enough convincing proof that the
Explanation of Solution
Given:
Formula used:
Calculation:
Conditions
The three conditions are: Random, independent.(10% condition), Normal/Large sample.
Random: Satisfied, because the sample is a random sample.
Independent: satisfied, because the sample of 10 patients who suffer from insomnia is less than 10% of the population of all patients who suffer from insomnia
Normal/ Large sample: satisfied, because the pattern in the normal quintile plot is roughly linear, this indicates that the distribution is about Normal.
Since all conditions are satisfied, it is suitable to perform a hypothesis test for the population mean
The mean is
The variance is
Hypothesis test
The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis statement is the population mean 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.
The statistic is
The P-value is the probability of getting the value of the test static, or a value more extreme, assuming that the null hypothesis is true.
Command Ti83/84- calculator: tcdf (3.051, 1E99, 9) which will return a P-value of 0.00689.Note: it could replace 1E99 by any other very large positive number.
If the P-value is smaller than the significance level
There is enough convincing proof that the mean sleep increase is positive for insomnia patients when taking the drug.
(b)
To Explain: the conclusion in part (a), which kind of mistakes a Type I error or a Type II error could have made, explain this mistake would mean in context.
(b)
Answer to Problem 74E
There is enough convincing proof that the mean sleep increase is positive for insomnia patients when taking this drug.
Explanation of Solution
In part (a), it is rejected the null hypothesis
Type I error: reject the null hypothesis
Type II error: Fail to reject the null hypothesis
Since we reject the null hypothesis
This would mean that there is enough convincing proof that the mean sleep increase is positive for insomnia patients when taking this drug, whereas the mean sleep increase is actually 0. This would then also imply that we would give insomnia patients a drug that doesn’t actually work.
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