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Mara Stratton
12/03/24 9:11 PM
n 11.1 Homework
Question 3, 11.1.17-T
HW Score: 50\%, 5 of 10 points
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In randomized, double-blind clinical trials of a new vaccine, rats 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, 113 of 748 subjects in the experimental group (group 1) experienced fever as a side effect. After the second dose, 70 of 629 of the subjects in the control group (group 2) experienced fever as a side effect. Does the evidence suggest that a higher proportion of subjects in group 1 experienced fever as a side effect than subjects in group 2 at the level of significance?
C. The samples are independent.
D. The samples are dependent.
E. The sample size is less than of the population size for each sample.
F. The data come from a population that is normally distributed.
Determine the null and alternative hypotheses.
Find the test statistic for this hypothesis test.
2.17 (Round to two decimal places as needed.)
Determine the P-value for this hypothesis test.
0.015 (Round to three decimal places as needed.)
Interpret the P -value.
If the population proportions are one would expect a sample difference proportion the one observed in about out of 1000 repetitions of this experiment.
(Round to the nearest integer as needed.)
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STEP 1
1. We are conducting a hypothesis test for two proportions.
2. The significance level is .
3. The null hypothesis is .
4. The alternative hypothesis is .
5. The samples are independent, and the sample size is less than 5% of the population size for each sample.
STEP 2
1. Calculate the test statistic.
2. Determine the P-value.
3. Interpret the P-value.
STEP 3
Calculate the test statistic using the formula for the difference in proportions:
where:
- is the sample proportion for group 1.
- is the sample proportion for group 2.
- is the pooled sample proportion.
STEP 4
Use the calculated test statistic to find the P-value. The test statistic is given as 2.17.
STEP 5
Interpret the P-value. The P-value is given as 0.015.
If the population proportions are equal, one would expect a sample difference proportion as extreme as the one observed in about 15 out of 1000 repetitions of this experiment.
The evidence suggests that there is a statistically significant difference in the proportion of subjects experiencing fever between the two groups at the level.
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