(2 points) (For the following question, you may use the "hand calculations" described in lecture. You must use at least four decimal places for all intermediate calculations and your final answer. If you use R prop.test0. please take the square-root of the X-squared value to get the 2 statistic for your answer!) A noted psychic was tested for ESP. The psychic was presented with 240 cards face down and was asked to determine if the card was one of 5 symbols: a star, cross, circle, square, or three wavy lines. The psychic was correct in 65 cases. Let p represent the probability that the psychic correctly identifies the symbol on the card in a random trial. Assume the 240 trials can be treated as an SRS from the population of all guesses. To see if there is evidence that the psychic is doing better than just guessing, we test H0 : p = .2 Ha 2 p > .2 (a) What is the z-statistic for this test? (b) What is the P-value of the test? (7 points) McBeans magazine recently published a news article about caffeine consumption in universities that claims that 80% of people at universities drink coffee regularly. Moonbucks, a popular coffee chain, is interested in opening a new store on WLU campus. After reading McBeans' article, they will consider opening a store in WLU if more than 80% of the people in WLU drink coffee regularly. A random sample of people from WLU was taken, and it was found that 680 out of 810 survey participants considered themselves as regular coffee drinkers. Does Moonbucks' survey result provide sufficient evidence to support opening a store at WLU? Part i) What is the parameter of interest? A. All people at WLU that drinks coffee regularly. B. Whether a person at WLU drinks coffee regularly. C. The proportion of people at WLU that drink coffee regularly out of the 810 surveyed. D. The proportion of all people at WLU that drink coffee regularly. Part ii) Let p be the population proportion of people at WLU that drink coffee regularly. What are the null and alternative hypotheses? A. Null: p = 0.80 . Alternative: p > 0.80 B. Null: p = 0.84 . Alternative: p > 0.84 C. Null: p = 0.84 . Alternative: p # 0.84 D. Null: p = 0.80 . Alternative: p = 0.84 E. Null: p = 0.84 . Alternative: p > 0.80 F. Null: p = 0.80 . Alternative: p # 0.80 Part iii) The P-value is found to be about 0.0025. Using all the information available to you, which of the following is/are correct? (check all that apply) A. Assuming the reported value 80% is correct, there is a 0.0025 probability that in a random sample of 810, at least 680 of the people at WLU regularly drink coffee. B. The observed proportion of people at WLU that drink coffee regularly is unusually high if the reported value 80% is correct. C. The reported value 80% must be false. D. The observed proportion of people at WLU that drink coffee regularly is unusually high if the reported value 80% is incorrect. E. Assuming the reported value 80% is incorrect, there is a 0.0025 probability that in a random sample of 810, at least 680 of the people at WLU regularly drink coffee F. The observed proportion of people at WLU that drink coffee regularly is unusually low if the reported value 80% is incorrect. G. The observed proportion of people at WLU that drink coffee regularly is unusually low if the reported value 80% is correct. Part iv) Based on the P -value (approximately 0.0025) obtained, at the 5% significance level, ... A. we should not reject the null hypothesis. B. we should reject the null hypothesis Part v) What is an appropriate conclusion for the hypothesis test at the 5% significance level? A. There is sufficient evidence to support opening a store at WLU. B. There is insufficient evidence to support opening a store at WLU. C. There is a 5% probability that the reported value 80% is true. D. Both A. and C. E. Both B. and C. Part vi) Which of the following scenarios describe the Type ll error of the test? A. The data do not provide sufficient evidence to support opening a store at WLU when in fact the true proportion of WLU people who drink coffee regularly is equal to the reported value 80%. B. The data provide sufficient evidence to support opening a store at WLU when in fact the true proportion of WLU people who drink coffee regularly is equal to the reported value 80% C. The data provide sufficient evidence to support opening a store at WLU when in fact the true proportion of WLU people who drink coffee regularly exceeds the reported value 80%. D. The data do not provide sufficient evidence to support opening a store at WLU when in fact the true proportion of WLU people who drink coffee regularly exceeds the reported value 80%. Part vii) Based on the result of the hypothesis test (at the 0.05 significance level), which of the following types of errors are we in a position of committing? A. Both Type I and Type II errors. B. Neither Type I nor Type II errors. C. Type I error only. D. Type II error only.(4 points) (For the following question, use the methods described in lecture - do not use R prop.test0. You must use at least four decimal places for all intermediate calculations and your final answer) A poll is taken in which 3610ut of 575 randomly selected voters indicated their preference for a certain candidate. (a) Find the "LargeSample" 99% condence interval for p. S p S (b) Find the margin of error for this 99% condence interval for p. (c) Without doing any calculations, indicate whether the margin of error is larger or smaller or the same for an 80% condence interval. A. smaller B. larger 0. same (3 points) (For the following question, use the methods described in lecture - do not use Fl prop.test0. You must use at least four decimal places for all intermediate claculations and your nal answer) A poll is taken in which 7 out of 26 randomly selected voters indicated their preference for a certain candidate. (a) Find the "Plus Four" 95% confidence interval for p. S p S (b) Find the margin of error for this "Plus Fciur'I 95% confidence interval for p