Question

An experimenter has prepared a drug-dose level that he claims will reduce hunger for 80% of people suffering from obesity. We feel that the claims regarding the effectiveness of his dosage are inflated (i.e., are too high). In attempt to prove this, we administer his prescribed dosage to 50 obese people and observe that 37 of them have had reduced hunger induced by the drug dose. Is there enough evidence to conclude that his claim is inflated at the 5% level of significance? (A) Yes, because the p-value is equal to .1446, which is greater than .05.   (B) Yes, because −1.06 is greater than −1.96.    (C) Yes, because 74% is less than 80% and the difference is more than 5%.   (D) No, because −1.06 is not less than −1.96. (E) No, because the p-value is equal to .1446, which is greater than .05.

Answer 1

solution:

The sample size is N = 50, the number of favorable cases is X = 37, and the sample proportion is

, and the significance level is α=0.05

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

This corresponds to a left-tailed test, for which a z-test for one population proportion needs to be used.

Based on the information provided, the significance level is α=0.05, and the critical value for a left-tailed test is

The rejection region for this left-tailed test is

Test Statistics

The z-statistic is computed as follows:

Decision about the null hypothesis

Since it is observed that , it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p=0.1444, and since , it is concluded that the null hypothesis is not rejected.

correct option:

c) no, because -1.06 is not less than -1.96.

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