A set of data items is normally distributed with a mean of 70 and a standard deviation of 8 . Convert 82 to a z-score. \( z_{82}=\square \) (Type an integer or a decimal.)

(b) Consider the hypotheses \( \mathrm{H}_{0}: \mu=103 \) versus \( \mathrm{H}_{1}: \mu>103 \). Explain what the director is testing. Perform the test at the \( \alpha=0.01 \) level of significance. Write a conclusion for the test. Explain what the director is testing. Choose the correct answer below. A. The director is testing if the sample provided sufficient evidence that the population mean IQ score is actually equal to 103 . B. The director is testing if the sample provided sufficient evidence that the population mean lQ score is actually not equal to 103 . The director is testing if the sample provided sufficient evidence that the population mean IQ score is actually not greater than 103 . C. Thesting if the sample provided sufficient evidence that the population mean lQ score is actually greater than 103 . Find the test statistic for this hypothesis test. (Round to two decimal places as needed.) an example

Suppose the mean IQ score of people in a certain country is 100 . Suppose the director of a college obtains a simple random sample of 42 students from that country and finds the mean IQ is 103.6 with a standard deviation of 13.5 . Complete parts (a) through (d) below. (a) Consider the hypotheses \( \mathrm{H}_{0}: \mu=100 \) versus \( \mathrm{H}_{1}: \mu>100 \). Explain what the director is testing. Perform the test at the \( \alpha=0.01 \) level of significance. Write a conclusion for the test. Explain what the director is testing. Choose the correct answer below. A. The director is testing if the sample provided sufficient evidence that the population mean IQ score is actually greater than 100 . C. The director is testing if the sample provided sufficient evidence that the population mean IQ score is actually equal to 100 . D. The director is testing if the sample provided sufficient evidence that the population mean IQ score is actually not equal to 100 . Find the test statistic for this hypothesis test. \( \square \) (Round to two decimal places as needed.)

Suppose the mean IQ score of people in a certain country is 100 . Suppose the director of a colle obtains a simple random sample of 40 students from that country and finds the mean IQ is 103.7 with a standard deviation of 13.6. Complete parts (a) through (d) below. B. The director is testing if the sample provided sufficient evidence that the population mean IQ score is actually not equal to 100 . The director is testing if the sample provided sufficient evidence that the population mear IQ score is actually greater than 100 . D. The director is testing if the sample provided sufficient evidence that the population mear IQ score is actually not greater than 100 . Find the test statistic for this hypothesis test. 1.72 (Round to two decimal places as needed.) Find the P-value for this hypothesis test. (Round to three decimal places as needed.)

(c) Consider the hypotheses \( \mathrm{H}_{0}: \mu=104 \) versus \( \mathrm{H}_{1}: \mu>104 \). Explain what the director is testing. Perform the test at the \( \alpha=0.01 \) level of significance. Write a Explain what the director is testing. Choose the correct answer below. A. The director is testing if the sample provided sufficient evidence that the population mean lQ score is actually not greater than 104 . The director is testing if the sample provided sufficient evidence that the population mean lQ score is actually greater than 104. C. The director is testing if the sample provided sufficient evidence that the population mean IQ score is actually not equal to 104 . D. The director is testing if the sample provided sufficient evidence that the population mean IQ score is actually equal to 104. Find the test statistic for this hypothesis test. 0.83 (Round to two decimal places as needed.) Find the P-value for this hypothesis test. \( \square \) (Round to three decimal places as needed.)

Find the test statistic for this hypothesis test. 1.72 (Round to two decimal places as needed.) Find the P-value for this hypothesis test. (Round to three decimal places as needed.) Set more help -