Question

In randomized, double-blind clinical trials of a new vaccine, monkeys were randomly divided into two groups. Subjects in group 1 received the new vaccine while subjects in group 2 received a control vaccine. After the second dose, 132 of 452 subjects in the experimental group (group 1) experienced drowsiness as a side effect. After the second dose, 39 of 103 of the subjects in the control group (group 2) experienced drowsiness as a side effect. Does the evidence suggest that a different proportion of subjects in group 1 experienced drowsiness as a side effect than subjects in group 2 at the alpha=0.10 level of significance? Determine the null and alternative hypotheses. Choose the correct answer below. A. ^ H 0 : p 1 = 0 versus ^ H 0 : p 1 not = 0 B. ^ H 0 : p 1 = p 2 versus ^ H 1 : p 1 not = p 2 C. ^ H 0 : p 1 = p 2 versus ^ H 1 : p 1 < p 2 D. ^ H 0 : p 1 = p 2 versus ^ H 1 : p 1 > p 2 The test statistic z 0 is negative 1.73. (Round to two decimal places as needed.) The P-value is 0.084. (Round to three decimal places as needed.) What is the result of this hypothesis test? A. Reject the null hypothesis because there is not sufficient evidence to conclude that a different proportion of subjects in group 1 experienced drowsiness as a side effect than subjects in group 2 at the alpha=0.10 level of significance.

Answer 1

The appropriate null and alternative hypotheses are that the proportions of subjects experiencing drowsiness in the two groups are equal and not equal, respectively. With a test statistic of -1.73 and a P-value of 0.084 at an alpha level of 0.10, the null hypothesis is rejected, suggesting that the proportions are different.

Step-by-step explanation:

The null and alternative hypotheses are important elements for hypothesis testing in statistics. In this case, to verify whether the proportions of subjects experiencing drowsiness after receiving vaccines differ between the two groups, the appropriate hypotheses would be:

• Null hypothesis (H0): p1 = p2
• Alternative hypothesis (H1): p1 ≠ p2

Given the presented test statistic z0 of -1.73 and a P-value of 0.084 with an alpha level of significance of 0.10, we compare the P-value with alpha to make a decision:

• If P-value < alpha: Reject the null hypothesis.
• If P-value ≥ alpha: Do not reject the null hypothesis.

Since the P-value of 0.084 is less than the significance level of 0.10, the decision would be to reject the null hypothesis. This means there is sufficient evidence at the alpha=0.10 level to suggest that the proportion of subjects experiencing drowsiness in group 1 is different from group 2.

Answer 2

The correct answer is B.

Therefore the appropiate null and alternative hypothesis are the following:

. H 0 : p 1 = p 2

H 1 : p 1 ≠ p 2

The aim of the test would be to conclude whether H0 should be rejected or not at a 10% significance level.

In this case a billateral significance test needs to be conducted, as such a test consists on testing the equality of the test value with a given value. In this case the H0 would be rejected if the test value is significanly different, both in the case that it is superior or inferior.

On the contrary, an unilateral significance test would have been conducted if aiming to check whether a value is superior or equal to the test value (left unilateral) or inferior or equal to this value (right unilateral).

Then, the result of the test is the one stated: rejecting H0 at the 10% significance level.