Smart Driver Driving School has many branches across provinces. In a province different from the one in problem 1, the teaching committee at the provincial branch randomly assigned half of their 5000 students enrolled this year to receive the conventional teaching method and the remaining half to receive the new teaching method. In a random sample of 100 students who received the conventional teaching method, 77 passed the road test. In another random sample of 100 students who received the new teaching method, 83 passed the road test. The committee would like to use the sample data to test if the two teaching methods have different passing rates. Let pC and pN be the true passing rates of the conventional and the new teaching methods, respectively. Part i) What are the appropriate null and alternative hypotheses? A. H0:pC−pN=0 and HA: pC−pN>0 B. H0:pN=0.77 and HA:pN≠0.77 C. H0:pC−pN=0 and HA:pC−pN≠0 D. H0:pC−pN=0 and HA:pC−pN<0 Part ii) The committee decides to perform the hypothesis test at 10% significance level. Which of the following is/are true? (Check all that apply.) A. There is 10% chance that the null hypothesis is true. B. The probability of committing the Type II error is 90%. C. The Type II error is 90%. D. The probability of committing the Type I error is 10%. E. The Type I error is 10%. F. There is 10% chance to reject the null hypothesis. G. None of the above. Part iii) Which of the following assumptions and conditions are needed to carry out the hypothesis test? CHECK ALL THAT APPLY. A. The two random samples are no larger than 10% of their respective population sizes. B. The two random samples of students are independent. C. The population sizes are sufficiently large. D. The variable whether a student passes or not follows the Normal model. E. None of the above.
Smart Driver Driving School has many branches across provinces. In a province different from the one in problem 1, the teaching committee at the provincial branch randomly assigned half of their 5000 students enrolled this year to receive the conventional teaching method and the remaining half to receive the new teaching method. In a random sample of 100 students who received the conventional teaching method, 77 passed the road test. In another random sample of 100 students who received the new teaching method, 83 passed the road test. The committee would like to use the sample data to test if the two teaching methods have different passing rates. Let pC and pN be the true passing rates of the conventional and the new teaching methods, respectively.
Part i) What are the appropriate null and alternative hypotheses?
A. H0:pC−pN=0 and HA: pC−pN>0
B. H0:pN=0.77 and HA:pN≠0.77
C. H0:pC−pN=0 and HA:pC−pN≠0
D. H0:pC−pN=0 and HA:pC−pN<0
Part ii) The committee decides to perform the hypothesis test at 10% significance level. Which of the following is/are true? (Check all that apply.)
A. There is 10% chance that the null hypothesis is true.
B. The probability of committing the Type II error is 90%.
C. The Type II error is 90%.
D. The probability of committing the Type I error is 10%.
E. The Type I error is 10%.
F. There is 10% chance to reject the null hypothesis.
G. None of the above.
Part iii) Which of the following assumptions and conditions are needed to carry out the hypothesis test? CHECK ALL THAT APPLY.
A. The two random samples are no larger than 10% of their respective population sizes.
B. The two random samples of students are independent.
C. The population sizes are sufficiently large.
D. The variable whether a student passes or not follows the Normal model.
E. None of the above.
Part iv) Construct a 95% confidence interval for the difference in the true passing rates (expressed as proportions) between the conventional and new teaching methods:
95% confidence interval: ( ,) [Your two numbers must be rounded to 3 decimal places. Keep at least 6 significant figures in intermediate steps.]
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