1. Out of 40 customers in shop, 25 bought plantains, 16 bought yam and 21 bought corns. Each of the customers bought at least one of the three items. Eight bought both plantain and yam, 11 bought plantain and corn and 6 bought yam and corn. (a) (i) Represent the information on a Venn diagram. (ii) How many customers bought all the three items? (iii) How many customers bought either plantain only or corn only? (ii) How many customers bought at least two items?

(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 -

(b) Consider the hypotheses \( \mathrm{H}_{0}: \mu=101 \) versus \( \mathrm{H}_{1}: \mu>101 \). 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 not equal to 101 . C. The director is testing if the sample provided sufficient evidence that the population mean IQ score is actually equal to 101 . D. The director is testing if the sample provided sufficient evidence that the population mean IQ score is actually not greater than 101 . Find the test statistic for this hypothesis test. 1.26 (Round to two decimal places as needed.) Find the P -value for this hypothesis test. (Round to three decimal places as needed.)

If the number 31 is added to the data set \( 3,5,6,6,8,11,12,22,26 \), by what value will the average of the data set increase?

If the number 31 is added to the data set \( 3,5,6,6,8,11,12,22,26 \), by what value will the average of the data set increase?