State the null and alternative hypotheses for the test. Compute the weighted est

Question

State the null and alternative hypotheses for the test. Compute the weighted estimate of the common population proportion. (Round your answers to 3 decimals.) Compute the value of the x test statistic. (Round your answers to 2 decimals.) Determine whether or not to reject the null hypothesis H_0. Be sure to show your work. A) Reject Null Hypothesis B) Fail to Reject Null Hypothesis Age of a person and their eye sight. Determine if the correlation between the two items given would be positive or negative or indicate if there is no correlation between the two items. A) Positive B) Negative C No correlation

Explanation / Answer

Solution:-

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 0.01. 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).

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

p = 0.205

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

SE = 0.0301

z = (p1 - p2) / SE

z = - 0.997

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 - 0.997 or greater than 0.997.

Thus, the P-value = 0.161 + 0.161 = 0.322

Interpret results. Since the P-value (0.322) is greater than the significance level (0.01), we have to accept the null hypothesis.

Fail to reject the null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that there is difference in proportion of men and women.

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