Question

In: Statistics and Probability

A state legislator wants to determine whether his voters' performance rating (00 - 100100) has changed...

A state legislator wants to determine whether his voters' performance rating (00 - 100100) 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%99% confidence interval for the true difference between the population means. Assume that the populations of voters' performance ratings are normally distributed for both this year and last year.

Rating (last year) 8383 8989 9191 7171 5656 7575 5959 4343 9292 7878
Rating (this year) 5454 8383 6868 7575 4949 8989 8080 6969 7272 5656

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Step 1 of 4:

Find the point estimate for the population mean of the paired differences. Let x1x1 be the rating from last year and x2x2 be the rating from this year and use the formula d=x2−x1d=x2−x1 to calculate the paired differences. Round your answer to one decimal place.

A state legislator wants to determine whether his voters' performance rating (00 - 100100) 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%99% confidence interval for the true difference between the population means. Assume that the populations of voters' performance ratings are normally distributed for both this year and last year.

Rating (last year) 8383 8989 9191 7171 5656 7575 5959 4343 9292 7878
Rating (this year) 5454 8383 6868 7575 4949 8989 8080 6969 7272 5656

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Step 2 of 4:

Calculate the sample standard deviation of the paired differences. Round your answer to six decimal places.

Solutions

Expert Solution

from above:

Step 1 of 4:

point estimate for the population mean of the paired differences =-4.2

Step 2 of 4:
sample standard deviation =19.696587

step 3:

for 99% CI; and 9 degree of freedom, value of t= 3.250
therefore confidence interval=sample mean -/+ t*std error
margin of errror          =t*std error=             20.242975

step 4:

lower confidence limit                     = -24.44
upper confidence limit                    = 16.04

(try -24.4 , 16.0 if required to one decimals)

orchestra answered 1 year ago
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