In the following scenario for a hypothesis test for a population mean, decide whether the z-test is an appropriate method for conducting the hypothesis test. Assume that the population standard deviation is known. Preliminary data analyses reveal that the sample data contain no outliers but that the distribution of the variable under consideration is probably mildly skewed. The sample size is 70. Choose the correct answer below. O A. The z-test is not an appropriate method, because the sample is not a large sample and the data are highly skewed. O B. The z-test is not an appropriate method, because the sample size is too small to be useful. O C. The z-test is an appropriate method, because the sample size is sufficiently large that the skewness of the variable does not matter. O D. The z-test is an appropriate method, because the sample contains no outliers.The mean length of imprisonment for motor-vehicle theft offenders in this country is 17.4 months. A hypothesis test is to be performed to decide whether the mean length of imprisonment in this city differs from the national mean. The null and alternative hypotheses are Ho: H = 17.4 months, Ha: H # 17.4 months. a. Explain what it would mean to make a type | error. O A. A type I error would occur if in fact u = 17.4 months, but the results of the sampling lead to the conclusion that u # 17.4 months. O B. A type I error would occur if in fact u # 17.4 months, but the results of the sampling fail to lead to the conclusion that u = 17.4 months. O C. A type I error would occur if in fact u = 17.4 months, but the results of the sampling fail to lead to the conclusion that u # 17.4 months. b. Explain what it would mean to make a type II error. O A. A type ll error would occur if in fact u = 17.4 months, but the results of the sampling lead to the conclusion that u # 17.4 months. O B. A type ll error would occur if in fact u # 17.4 months, but the results of the sampling fail to lead to the conclusion that p # 17.4 months. O C. A type ll error would occur if in fact u # 17.4 months, but the results of the sampling lead to the conclusion that u # 17.4 months. c. Explain what it would mean to make a correct decision. O A. A correct decision would occur if u = 17.4 months and the results of the sampling lead to the rejection of that fact; or if u # 17.4 months and the results of the sampling do not lead to that conclusion. O B. A correct decision would occur if u = 17.4 months and the results of the sampling do not lead to the rejection of that fact; or if u # 17.4 months and the results of the sampling lead to that conclusion. O C. A correct decision would occur if u # 17.4 months and the results of the sampling lead to the rejection of that fact; or if u = 17.4 months and the results of the sampling do not lead to that conclusion. d. Now suppose that the results of carrying out the hypothesis test lead to nonrejection of the null hypothesis. Classify that conclusion by error type or as a correct decision if in fact the mean length of imprisonment for motor-vehicle theft offenders in this city equals the national mean of 17.4 months. O A. Type II error O B. Correct decision O C. Type I errorThe mean length of imprisonment for motor-vehicle theft offenders in this country is 17.4 months. A hypothesis test is to be performed to decide whether the mean length of imprisonment in this city differs from the national mean. The null and alternative hypotheses are Ho: H = 17.4 months, Ha: H # 17.4 months. D. Atype I enol would occur It In fact + 17.4 morris, but we results of the sampling fall to read to the Conclusion That A - 17.4 moms. O C. A type I error would occur if in fact u = 17.4 months, but the results of the sampling fail to lead to the conclusion that p # 17.4 months. b. Explain what it would mean to make a type ll error. O A. A type ll error would occur if in fact u = 17.4 months, but the results of the sampling lead to the conclusion that p # 17.4 months. O B. A type ll error would occur if in fact u # 17.4 months, but the results of the sampling fail to lead to the conclusion that u # 17.4 months. O C. A type ll error would occur if in fact u # 17.4 months, but the results of the sampling lead to the conclusion that u # 17.4 months. c. Explain what it would mean to make a correct decision. O A. A correct decision would occur if u = 17.4 months and the results of the sampling lead to the rejection of that fact; or if u # 17.4 months and the results of the sampling do not lead to that conclusion. O B. A correct decision would occur if u = 17.4 months and the results of the sampling do not lead to the rejection of that fact; or if u # 17.4 months and the results of the sampling lead to that conclusion. O C. A correct decision would occur if u # 17.4 months and the results of the sampling lead to the rejection of that fact; or if u = 17.4 months and the results of the sampling do not lead to that conclusion. d. Now suppose that the results of carrying out the hypothesis test lead to nonrejection of the null hypothesis. Classify that conclusion by error type or as a correct decision if in fact the mean length of imprisonment for motor-vehicle theft offenders in this city equals the national mean of 17.4 months. O A. Type II error O B. Correct decision O C. Type I error e. Suppose that the results of carrying out the hypothesis test lead to nonrejection of the null hypothesis. Classify the conclusion by error type or as a correct decision if in fact the mean length of imprisonment for motor-vehicle theft offenders in this city differs from the national mean of 17.4 months. O A. Correct decision O B. Type II error O C. Type | errorA sample mean, sample size, and population standard deviation are provided below. Use the one-mean z-test to perform the required hypothesis test at the 1% significance level. x = 33, n= 24, 0 =8, Ho: H= 35, Ha: H# 35 The test statistic is z =]. (Round to two decimal places as needed.) The P-value is. (Round to three decimal places as needed.) the null hypothesis. The data sufficient evidence to conclude that the mean isA sample mean, sample size, and population standard deviation are provided below. Use the one-mean z-test to perform the required hypothesis test at the 1% significance level. x =33, n= 24, 0 =8, Ho: H=35, Ha: HI# 35 The test statistic is z =]. (Round to two decimal places as needed.) The P-value is]. (Round to three decimal places as needed.) the null hypothesis. The data sufficient evidence to conclude that the mean is Reject Do not rejectA sample mean, sample size, and population standard deviation are provided below. Use the one-mean z-test to perform the required hypothesis test at the 1% significance level. x =33, n =24, 0 =8, Ho: H=35, Ha: |# 35 The test statistic is z =]. (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.) the null hypothesis. The data sufficient evidence to conclude that the mean is do not provide provideA sample mean, sample size, and population standard deviation are provided below. Use the one-mean z-test to perform the required hypothesis test at the 1% significance level. x =33, n= 24, 0 =8, Ho: H = 35, Ha: H# 35 The test statistic is z =]. (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.) the null hypothesis. The data sufficient evidence to conclude that the mean is greater than 35. not equal to 35. less than 35. equal to 35.P-value Evidence against Ho For the given P-value, refer to the table to determine the strength of the evidence against the null hypothesis. P > 0.10 Weak or none P = 0.09 0.05 0.10 Weak or none P = 0.09 0.05 0.10. 0.01