Determine whether a normal sampling distribution can be used for the following sample statistics. If it can be used, test the claim about the difference between two population proportions p1 and p2 at the level of significance ?. Assume that the samples are random and independent. Claim: p1 ? p2, ? = 0.01 Sample Statistics: x1 = 38, n1 = 74, x2 = 37, n2 = 69 Determine whether a normal sampling distribution can be used. The samples are random and independent. A normal sampling distribution [ ] be used because n1p? = [ ], n1q? = [ ], n2p? = [ ], and n2q? = [ ]. (Round to two decimal places as needed.) State the null and alternative hypotheses, if applicable. A. H0: p1 ? p2 Ha: p1 > p2 B. H0: p1 ? p2 Ha: p1 < p2 C. H0: p1 = p2 Ha: p1 ? p2 D. The conditions to use a normal sampling distribution are not met. Calculate the standardized test statistic for the difference p1 - p2, if applicable. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. P = [ ] (Round to three decimal places as needed.) B. The conditions to use a normal sampling distribution are not met. State the conclusion of the hypothesis test, if applicable. Choose the correct answer below. A. Since P < ?, reject H0. There is enough evidence at the ? = 0.01 level of significance to support the claim. B. Since P > ?, fail to reject H0. There is not enough evidence at the ? = 0.01 level of significance to support the claim. C. Since P > ?, reject H0. There is enough evidence at the ? = 0.01 level of significance to support the claim. D. Since P < ?, fail to reject H0. There is not enough evidence at the ? = 0.01 level of significance to support the claim. E. The conditions to use a normal sampling distribution are not met.
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- Calculate the sample proportions: \[ \hat{p}_1 = \frac{x_1}{n_1} = \frac{38}{74} \approx 0.514 \] \[ \hat{p}_2 = \frac{x_2}{n_2} = \frac{37}{69} \approx 0.536 \] - Calculate the pooled sample proportion: \[ \bar{p} = \frac{x_1 + x_2}{n_1 + n_2} Show more…
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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 ̑̑̑ using the given sample statistics. Assume the sample statistics are from independent random samples. Claim: p1 = p2, ̑̑̑ = 0.01 Sample statistics: x1 = 74, n1 = 147 and x2 = 148, n2 = 221 A. H0: p1 = p2, Ha: p1 > p2 B. H0: p1 = p2, Ha: p1 ≠ p2 C. H0: p1 ≠ p2, Ha: p1 = p2 D. H0: p1 < p2, Ha: p1 = p2 E. A normal sampling distribution cannot be used, so the claim cannot be tested. Find the critical values. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The critical values are -z0 = [ ] and z0 = [ ]. (Round to two decimal places as needed.) B. A normal sampling distribution cannot be used, so the claim cannot be tested.
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Determine whether a normal sampling distribution can be used for the following sample statistics. If it can be used, test the claim about the difference between two population proportions p1 and p2 at the level of significance ̑. Assume that the samples are random and independent. Claim: p1 ≠ p2, ̑ = 0.01 Sample Statistics: x1 = 37, n1 = 69, x2 = 38, n2 = 74 Determine whether a normal sampling distribution can be used. The samples are random and independent. A normal sampling distribution be used because n1p̄ =, n1q̄ =, n2p̄ =, and n2q̄ =. (Round to two decimal places as needed.)
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