Question

A large statistics class consists of 250 students. On the final exam, the professor worries that question 13 might be unfair. He resolves to drop question 13 if less than 40% of the class correctly answers the question. After grading 125 randomly selected final exams (out of 250 taken), a student calls the professor and asks if question 13 will be dropped. The professor looks at the graded exams and notes that 46 of the 125 graded exams got question 13 correct. Based on this partial information, the professor will create an 84% confidence interval for the proportion of the entire class of 250 students that correctly answered question 13 on the final in order to assess whether it is likely he will drop that question.

2pts

1. Identify the population and, in the context of the problem, identify a

“success”.

Population: _____________________________

Success: ________________________________

2pts

2. Find the 84% confidence interval for the proportion of the entire class that correctly answered question 13.

Note: CF is important here

_______________________________________________________

3. Based on the interval formed above, can the professor confidently conclude that question 13 will be dropped? ________                                                          AND WHY ?   ___________________________________________________

4. Suppose the professor has an assistant that is assigned to grade the other half of the exams. If the professor asks the assistant to grade the other 125 exams and use the data to also create an 84% confidence interval for the proportion of students correctly answering question 13 in the class, what is the chance the interval the assistant creates will contain the true percentage of students in the entire class correctly answering question 13? _________________

Answer 1

(a) Population: All the students in the statistics class

Success: 46 out of 125 students in the statistics class who got question 13 correct

(b) p̂ = 46/125 = 0.368

The 84% confidence interval will be:

= p ± z*(√p(1-p)/n)

= 0.368 ± 0.99*(√0.368(1-0.368)/125)

= (0.3074, 0.4286)

(c) Since the confidence interval contains 0.40, question 13 will not be dropped.

(d) We can be 84% confident that the true percentage of students in the entire class correctly answering question 13 will be in the confidence interval.

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