Question

A state legislator wants to determine whether his voters' performance rating (0 - 100) has changed from last year to this year. The following table shows the legislator's performance from the same ten randomly selected voters for last year and this year. Use this data to find the 99% confidence interval for the true difference between the population means. Let d=(this year's rating)−(last year's rating). Assume that the populations of voters' performance ratings are normally distributed for both this year and last year.

Rating (last year) 50 59 48 45 40 75 66 81 53 70

Rating (this year) 42 52 42 75 59 81 87 61 56 91

Step 1 of 4: Find the mean of the paired differences, d‾‾. Round your answer to one decimal place.

Step 2 of 4: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Step 3 of 4: Find the standard deviation of the paired differences to be used in constructing the confidence interval. Round your answer to one decimal place.

Step 4 of 4: Construct the 99% confidence interval. Round your answers to one decimal place.

Answer 1

The statistical software output for this problem is:

Hence,

Step - 1: Mean = 5.9

Step - 2: Critical value = 3.250

Step - 3: Standard deviation = 16.3

Step - 4: 99% confidence interval will be:

Lower limit = -10.8

Upper limit = 22.6

answered by: anonymous