This Question: 1 pt 20 of 30 (10 complete) This Quiz: 30 pts possible Question H

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This Question: 1 pt 20 of 30 (10 complete) This Quiz: 30 pts possible Question Help Decide whether the normal sampling distribution can be used. If it can be used, test the claim about the difference between two population proportions p1 and p2 at the given level of significance or using the given sample statistics. Assume the sample statistics are from independent random samples p1-p2, . 0.10 x1 = 44, n1 = 101 and x2 = 164, n2-225 Claim: Sample statistics: Can a normal sampling distribution be used? O No O Yes Identify the null and altenative hypotheses. Choose the correct answer below. Ha: p1 =p2 Ha: p1 #p2 Ha: p1 = p2 Ho:P1=P2 Ha P1 P2 A normal sampling distribution cannot be used, so the claim cannot be tested. OD. 0 E. Find the critical values. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. o A. The critical values are-zo- Round to two decimal places as needed.) A normal sampling distribution cannot be used, so the claim cannot be tested. and zo = O B. Find the standardized test statistic. Select the correct choice below and, if necessary, fill in the answer box to complete your choice 0 A. z-I (Round to two decimal places as needed.) O B. A normal sampling distribution cannot be used, so the claim cannot be tested State the conclusion. Choose the correct answer below 0 A. O B. ° C. 0 D. O E. Reject Ho . There is sufficient evidence that there is a difference between p1 and p2 Fail to reject Ho. There is sufficient evidence that there is a difference between p1 and p2 Fail to reject Ho . There is insufficient evidence that there is a difference between p1 and p2 Reject Ho . There is insufficient evidence that there is a difference between p1 and p2 A normal sampling distribution cannot be used, so the claim cannot be tested

Explanation / Answer

Solution:-

Yes, normal distribution can be used.

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P1 = P2

Alternative hypothesis: P1 P2

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the proportion from population 1 is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a two-proportion z-test.

Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).

zcritical = + 1.645

Rejection region is - 1.645 > z > 1.645

p = (p1 * n1 + p2 * n2) / (n1 + n2)

p = 0.638

SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }

SE = 0.0576

z = (p1 - p2) / SE

z = - 5.09

where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.

Since we have a two-tailed test, the P-value is the probability that the z-score is less than - 5.09 or greater than 5.09.

Thus, the P-value = less than 0.0001.

Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we cannot accept the null hypothesis.

Reject H0, there is sufficient evidence that there is difference in two proportions.

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