a. $H_0: P_1 - P_2 = 0$ $H_a: P_1 - P_2 \neq 0$ Sample 1 Sample 2 $n_1 = 374$ $n_2 = 400$ $x_1 = 172$ $x_2 = 183$ Let $\alpha = .05$. Note that x is the number in the sample having the characteristic of interest. b. $H_0: P_1 - P_2 = 0$ $H_a: P_1 - P_2 > 0$ Sample 1 Sample 2 $n_1 = 659$ $n_2 = 559$ $\hat{P}_1 = 0.36$ $\hat{P}_2 = 0.25$ Let $\alpha = .10$. Appendix A Statistical *(Round the intermediate values to 3 decimal places, e.g. 1.254. Round your answer to 2 decimal places, e.g. 15.25.) **(Round the intermediate values to 2 decimal places, e.g. 15.25. Round your answer to 2 decimal places, e.g. 15.25.) a. Observed z = The decision is to fail to reject the null hypothesis
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This is the level at which we are willing to reject the null hypothesis. Common significance levels include 0.05 and 0.01. Show more…
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Decide to Reject H0 or Not Reject H0 using the classical method (see p374) and the p-value method (see p368) of the Navidi/Monk book. H0: mu = 15.4 H1: mu < 15.4 alpha = 0.05 where n = 30, x̄ = 14.6, s = 3.7 Compute the sample t (using the above formula) to 3 decimal places and include a minus sign in front of it if it is negative. Answer: -1.184 Refer to the significance test in problem #1 and enter the area that goes into the appropriate tail of the distribution as a decimal to 2 places. Answer: Refer to the test in problem #1, and enter the p-value estimate (each to 2 decimals). For example: if df = 16 and 2.235 < 2.251 < 2.583, the areas at the top of the table would be 0.02 and 0.01, making a one-tailed estimate for p, so you would enter 0.01<p<0.02 with no spaces in between. Answer: 0.020<p<0.050
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A sample of 50 observations is selected from a normal population. The sample mean is 65, and the population standard deviation is 4. Conduct the following test of the hypothesis using the 0.05 significance level. H0: μ = 66 H1: μ ≠ 66 a. Is this a one- or two-tailed test? multiple choice 1 One-tailed test Two-tailed test b. What is the decision rule? multiple choice 2 Reject H0 if −1.960 < z < 1.960 Reject H0 if z < −1.960 or z > 1.960 c. What is the value of the test statistic? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) Value of the test statistic d. What is your decision regarding H0? multiple choice 3 Reject H0 Fail to reject H0 e-1. What is the p-value? (Round your z value to 2 decimal places and final answer to 4 decimal places.) p-value e-2. Interpret the p-value? (Round your z value to 2 decimal places and final answer to 2 decimal places.) There is a % chance of finding a z value this large by “sampling error” when H0 is true.
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A sample of 39 observations is selected from one population with a population standard deviation of 5. The sample mean is 100. A sample of 52 observations is selected from a second population with a population standard deviation of 7. The sample mean is 98. Conduct the following test of hypothesis using the 0.1 significance level: H0: μ1 – μ2 = 0 H1: μ1 – μ2 ≠ 0 a. Is this a one-tailed or a two-tailed test? Two b. State the decision rule. (Negative answer should be indicated by a minus sign. Round the final answers to 2 decimal places.) The decision rule is to reject H0 if z is outside the interval ( , ). c. Compute the value of the test statistic. (Round the final answer to 2 decimal places.) Value of the test statistic d. What is your decision regarding H0? Do not reject H0. e. What is the p-value? (Round the z-value to 2 decimal places. Round the final answer to 4 decimal places.) The p-value is .
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