For each of the situations in parts a through d below, state whether a Type I, a Type II, or neither error has been made. Explain briefly. 18 a) A bank wants to know if the enrollment on their website is above 30% based on a small sample of customers. They test Ho: p = 0.3 vs. H: p>0.3 and reject the null hypothesis. Later they find out that actually 28% of all customers enrolled. Choose the correct answer below. A. The bank made a Type I error. The actual value is close to 0.3 but they rejected the null hypothesis. B. The bank made a Type II error. The actual value is close to 0.3 but they rejected the null hypothesis. C. The bank made a Type I error. The actual value is not greater than 0.3 but they rejected the null hypothesis. OD. The bank did not make an error. The actual value is not equal to 0.3 and they rejected the null hypothesis. E. The bank made a Type II error. The actual value is not greater than 0.3 but they rejected the null hypothesis. b) A student tests 100 students to determine whether other students on her campus prefer soda brand A or soda brand B and finds no evidence that preference for brand A is not 0.5. Later, a marketing company tests all students on campus and finds no difference. Choose the correct answer below. A. The student made a Type I error. She did not reject the null hypothesis. B. The student made a Type I error. She found no evidence that preference for brand A is not a certain value, but the marketing company found no evidence that preference for brand A is a certain value. C. The student made a Type II error. She did not reject the null hypothesis. D. The student did not make an error. The actual value is 0.50, which was not rejected. E. The student made a Type II error. She found no evidence that preference for brand A is not a certain value, but the marketing company found no evidence that preference for brand A is a certain value. c) A human resource analyst wants to know if the applicants this year score, on average, higher on their placement exam than the 52.5 points the candidates averaged last year. She samples 50 recent tests and finds the average to be 54.1 points. She fails to reject the null hypothesis that the mean is 52.5 points. At the end of the year, they find that the candidates this year had a mean of 55.3 points. Choose the correct answer below. A. The analyst made a Type II error. The actual value was 55.3 points, which is greater than 52.5. B. The analyst made a Type I error. The actual value was 55.3 points, which is close to 52.5. C. The analyst made a Type I error. The actual value was 55.3 points, which is greater than 52.5. D. The analyst did not make an error. The actual value was 55.3 points, which is close to 52.5. E. The analyst made a Type II error. The actual value was 55.3 points, which is close to 52.5. d) A pharmaceutical company tests whether a drug lifts the headache relief rate from the 25% achieved by the placebo. They fail to reject the null hypothesis because the P-value is 0.465. Further testing shows that the drug actually relieves headaches in 38% of people. Choose the correct answer below. A. The company made a Type II error. It used a P-value to determine its conclusion instead of a critical value. B. The company did not make an error. They did not reject the null hypothesis when the P-value was almost 0.5. OC. The company made a Type II error. The null hypothesis was not rejected, but it was false. The true relief rate was greater than 0.25. OD. The company made a Type I error. The null hypothesis was not rejected, but it was false. The true relief rate was greater than 0.25. E. The company made a Type I error. It used a P-value to determine its conclusion instead of a critical value.