In: Statistics and Probability
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? |
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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.
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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.