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) 6969 8181 7676 6363 6464 6565 6969 9595 9292 6060 Rating (this year) 4444 8484 6767 6060 8787 9494 4040 7676 7777 7676 Step 1 of 4: Find the point estimate for the population mean of the paired differences. Let x1�1 be the rating from last year and x2�2 be the rating from this year and use the formula d=x2−x1�=�2−�1 to calculate the paired differences. Round your answer to one decimal place. Step 2 of 4: Calculate the sample standard deviation of the paired differences. Round your answer to six decimal places. Step 3 of 4: Calculate the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places. Step 4 of 4: Construct the 99%99% confidence interval. Round your answers to one decimal place

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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)	6969	8181	7676	6363	6464	6565	6969	9595	9292	6060
Rating (this year)	4444	8484	6767	6060	8787	9494	4040	7676	7777	7676

Step 1 of 4:

Find the point estimate for the population mean of the paired differences. Let x1�1 be the rating from last year and x2�2 be the rating from this year and use the formula d=x2−x1�=�2−�1 to calculate the paired differences. Round your answer to one decimal place.

Step 2 of 4:

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

Step 3 of 4:

Calculate the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.

Step 4 of 4:

Construct the 99%99% confidence interval. Round your answers to one decimal place.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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