12. You found that the null hypothesis μ1- μ2 ≤ 100 could not be rejected at a = 0.05. If the same sample is used, which of the following is correct?
(A)H₀:μ1- μ2 ≤ 95 can never be rejected at a = 0.05;
(B)H0:μ1- μ2 ≤ 105 can never be rejected at a = 0.01;
(C) H₀: μ1- μ2 ≤ = 100 can never be rejected at a = 0.05;
(D) Insufficient data to claim any of the above.

1.Suppose we have a population that is normally distributed, and its standard deviation is unknown. We want to test the following hypotheses: H0:μ=12 vs Ha:μ≠12. If the value of the test statistic is -1.9 based on a sample of size 20, what type of test statistic is it and what is the corresponding p-value? (A)z statistic, 0.0287; (B)z statistic, 0.0574; (C) t statistic, between 0.025 and 0.05; (D) t statistic, between 0.05 and 0.10.

2. To test the null hypothesisH0:μ=12 , which alterative hypothesis of following would have the highest testing power? (A)Ha:μ=10; (B)Ha:μ=12; (C) Ha:μ=15; (D) It depends on the sample size.

3.To test the bypotheses H0:μ=12 vs Ha:μ=10, which following sample size would end up to be the lowest testing power with the specified a = 0.05? (A)n=20; (B)n=30; (C) n=100; (D) It depends on the sample observations.

4. Suppose p-value is equal to 0.0626. The null hypothesis can be rejected (A)if a=0.10 in a two-tailed test; (B)if a= 0.05 in a two-tailed test; (C) if a = 0.05 in a one-tailed test； (D) Not enough information to make a conclusion.

5. In a two-tailed test for population mean u, suppose the p-value is equal to 0.0626. Which one of the following statements is not true? (A)The 90% confidence interval of u contains the hypothesized value uo； (B) The 95% confidence interval of u contains the hypothesized value 4o； (C) The 99% confidence interval of u contains the hypothesized value [4o； (D) The testing power is not determined by p-value.

5. In a two-tailed test for population mean u, suppose the p-value is equal to 0.0626. Which one of the following statements is not true? (A)The 90% confidence interval of u contains the hypothesized value uo; (B)The 95% confidence interval of u contains the hypothesized value po; (C) The 99% confidence interval of u contains the hypothesized value po; (D) The testing power is not determined by p-value.

6.Which of the following statements is not true about the level of significance for a hypothesis test? (A)The level of significance is usually denoted by alpha (a); (B) If the p-value is less than the level of significance, we reject the null hypothesis; (C) The level of significance is the maximum allowable probability of making a Type I error; (D) The level of significan nce is determined by the valuc of the test statistic.

7. Which of the following is incorrect for the linear regression model y= β0 + β1x+ε and its predictive equation , if the sample observations are not specified? (A)b0 and b1 are random variables; (B)β0 and  β1 are random variables; (C) yand ε are random variables; (D) is a random variable.

8. Based on the assumptions of an ANO VA procedure, which of the following cannot be determined? (A) The distributions of the populations; .(B)Whether the samples are independent or not; (C) Whether all the population means are different; (D) The variance of the other populations if the variance of one population is known as 10.

9.We have a population that is normally distributed with an unknown variance. A two-tailed hypothesis test was conducted for the population mean. A random sample of size 22 was selected. After setting the level of significance, a, a student wrongly used as the critical value and concluded to reject the null hypothesis. If the student did not make the mistake, what would be the correct conclusion? (A)The conclusion stays the same, that is, the null hypothesis should be rejected; (B)The conclusion is different, that is, the null hypothesis should not be rejected; (C) There is insufficient information to make a conclusion. In other words, the null hypothesis may or may not be rejected; (D) None of the above.

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