Answered: A) Test the claim using a hypothesis…

Name: Identify the null hypothesis, alternative hypothesis, test statistic,
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Description: Identify the null hypothesis, alternative hypothesis, test statistic, critical value(s), P-value (range of P-value), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Assume that the two samples are indepen

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 58E: What is meant by the sample space of an experiment?

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Identify the null hypothesis, alternative hypothesis, test statistic, critical value(s), P-value (range of P-value), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Assume that the two samples are independent simple random samples selected from normally distributed populations.

The drug Clarinex is used to treat symptoms from allergies. In a clinical trial of this drug, 2.1% of the 1655 treated subjects experienced fatigue. Among the 1652 subjects given placebos, 1.2% experienced fatigue. Use a 0.05 significance level to test the claim that the incidence of fatigue is greater among those who use Calrinex.

A) Test the claim using a hypothesis test.
B) Construct an appropriate confidence interval.

I don't know which one to use in the TI 84 Calculator. I was going to use 2propztest but it wasn't working because there is no x bar in the equation the equation only has N and P hat (I think)

Expert Solution

Step 1

For sample 1, we have that the sample size is $N_1= 1655$ , the number of favorable cases is $X_1 = 35$ , so then the sample proportion is $\hat p_1 = \frac{X_1}{N_1} = \frac{ 35}{ 1655} = 0.0211$

For sample 2, we have that the sample size is $N_2 = 1652$ , the number of favorable cases is $X_2 = 20$ , so then the sample proportion is $\hat p_2 = \frac{X_2}{N_2} = \frac{ 20}{ 1652} = 0.0121$

The value of the pooled proportion is computed as $\bar p = \frac{ X_1+X_2}{N_1+N_2}= \frac{ 35 + 20}{ 1655+1652} = 0.0166$

Also, the given significance level is $\alpha = 0.05$

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

$Ho: p_1 = p_2$

$H a : p_{1} > p_{2}$

This corresponds to a right-tailed test, for which a z-test for two population proportions needs to be conducted.

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A) Test the claim using a hypothesis test. B) Construct an appropriate confidence interval.