Question

1)A matched pairs design is often used to compare two products such as colas. Each subject tastes both colas in random order without knowing which cola he/she is tasting. The subject then selects his/her preferred cola. Suppose 64% of 75 subjects preferred brand A.

A) What is the p-value for the hypothesis test of no brand preference?

a) 0.64

b)0.05

c) 0.015

d) 0.008

B) What sample size would be needed to ensure that the margin of error in the brand preference is less than 5 percentage points in more than 95% of experiments?

a)20

b)385

c)40

d)1500

2)Two polls of the electorate were taken a week apart. In the first week, support for the leading party was 60% with a 95% margin of error of 3 percentage points. In the second week, support for the same party was 57% with a 95% margin of error of 3 percentage points. Which statement is correct?

a) Because the change in support between the two weeks is less than the margin of error, there is no evidence of a change in support. b) There is a 3% chance of change in party support between the two weeks. c) We are 95% confident that the change in party support is 3 percentage points. d)There is a 5% chance that the change in party support is not real.

Answer 1

Solution: A) What is the p-value for the hypothesis test of no brand preference?

Answer: C. 0.015

Explanation:

To find the p-value, we need to first find the test statistic:

The test statistic is given below:

  

  

Therefore,

Using the standard normal table, we have:

Therefore, the correct option is C. 0.015

B) What sample size would be needed to ensure that the margin of error in the brand preference is less than 5 percentage points in more than 95% of experiments?

Answer: b)385

Explanation:

Where:

is the margin of error

is the critical value at 0.05 significance level

2)Two polls of the electorate were taken a week apart. In the first week, support for the leading party was 60% with a 95% margin of error of 3 percentage points. In the second week, support for the same party was 57% with a 95% margin of error of 3 percentage points. Which statement is correct?

Answer: a) Because the change in support between the two weeks is less than the margin of error, there is no evidence of a change in support.