Question

1. A random sample of 20 students yielded a mean of ¯x = 72 and a variance of s 2 = 16 for scores on a college placement test in mathematics. Assuming the scores to be normally distributed, construct a 98% confidence interval for σ 2 . Be sure to

• State if the problem involves 1 population or 2 populations. If you have 2 populations, should they be paired or not?

• State α.

• State whether you should use z, t, or χ 2 and find / provide the appropriate value(s) from the table (or your calculator).

• Find the confidence interval. Round your final values to 3 decimals. • Write a verbal interpretation of your confidence interval.

2. Problem Setup:

A very large study showed that aspirin reduced the rate of heart attacks by 44%. A pharmaceutical company thinks they have a drug that will be more effective than aspirin, and plans to do a randomized clinical trial to test the new drug.

Your Questions:

(a) What is the null hypothesis the company will use?

(b) What is their alternative hypothesis?

Questions 1&2

Answer 1

1 ) The 98 % confidence interval for is :

where ,

Required confidence interval :

The problem only involves one population .

We are 98 % confident that the value of the population variance will lie in the interval given by

2 ) To test :

Null hypothesis :

Alternative hypothesis :