A state legislator wants to determine whether his voters' performance rating (0 - 100)(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 95%95% confidence interval for the true difference between the population means.Let d=(this year's rating)−(last year's rating)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)60408478787752664969Rating (this year)66535461558374524471Step 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 95% confidence interval. Round your answers to one decimal place.

Given: n = 10 Confidence level = 95% Formula Used: Confidence Interval = d ± t*sdn

Answered: A state legislator wants to determine…

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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A state legislator wants to determine whether his voters' performance rating (0 - 100)(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 95%95% confidence interval for the true difference between the population means.

Let d=(this year's rating)−(last year's rating)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)	60	40	84	78	78	77	52	66	49	69
Rating (this year)	66	53	54	61	55	83	74	52	44	71

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 95% 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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