1) Inferences About the Difference Between Two Population Means: Matched Samples

In order to determine whether or not a motorcycle education course improves the scores on a driving exam, a sample of 6 drivers were given the exam before and after taking the course. The results are shown below.Assume the population of differences is normally distributed.

Let d = Score After - Score Before.

Score

Before the Course

83

89

93

77

86

79

Score

After the Course

87

89

91

77

93

83

a. Compute the test statistic.

b. Using = .05and the p-value approach, test to see if taking the course actually increased scores on the driving exam.

2) Population Proportion

A new coffee drink called the Raktajino is being market tested. Four hundred customers were given the new drink to try. The consumers were asked whether they liked or disliked the drink bar. You are given their responses below.

Response Frequency

Liked 300

Disliked 100

400

a. What is the point estimate for the proportion of people who liked the Raktajino?

b. Construct a 97% confidence interval for the true proportion of people who liked the new drink.

c. With a .97 probability, how large of a sample needs to be taken to provide a margin of error of 4% or less?