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Name: In order to ensure that there is not a large disparity in the quality
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Description: In order to ensure that there is not a large disparity in the quality of education at various schools in a school district, the school board wants to make sure that the variance of the mean standardized-test scores for all students at each school in

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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In order to ensure that there is not a large disparity in the quality of education at various schools in a school district, the school board wants to make sure that the variance of the mean standardized-test scores for all students at each school in the district is less than 2. To test this claim, they looked at the mean student scores for the standardized test from a random sample of 27 schools in the district. The results from the survey found that the overall mean was a score of 209.740 with a standard deviation of 1.210. With α=0.05, perform a hypothesis test to determine if the variance is less than 2. Assume that the district standardized-test scores are normally distributed.

Step 3 of 3 : Draw a conclusion and interpret the decision.

1. We reject the null hypothesis and conclude that there is sufficient evidence at a 0.05 level of significance that the variance of the mean standardized-test scores for all students at each school in the district is less than 2.

2. We reject the null hypothesis and conclude that there is insufficient evidenceat a 0.05 level of significance that the variance of the mean standardized-test scores for all students at each school in the district is less than 2.

3. We fail to reject the null hypothesis and conclude that there is insufficient evidenceat a 0.05 level of significance that the variance of the mean standardized-test scores for all students at each school in the district is less than 2.

4. We fail to reject the null hypothesis and conclude that there is sufficient evidenceat a 0.05 level of significance that the variance of the mean standardized-test scores for all students at each school in the district is less than 2.

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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