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A factor in determining the usefulness of an examination as a measure of demonstrated ability is the amount of spread that occurs in the grades. If the spread or variation of examination scores is very small, it usually means that the examination was either too hard or too easy. However, if the variance of scores is moderately large, then there is a definite difference in scores between "better," "average," and "poorer" students. A group of attorneys in a midwestern state has been given the task of making up this year's bar examination for the state. The examination has 500 total possible points, and from the history of past examinations, it is known that a standard deviation of around 60 points is desirable. Of course, too large or too small a standard deviation is not good. The attorneys want to test their examination to see how good it is. A preliminary version of the examination (with slight modifications to protect the integrity of the real examination) is given to a random sample of 20 newly graduated law students. Their scores give a sample standard deviation of 73 points. Using a 0.01 level of significance, test the claim that the population standard deviation for the new examination is 60 against the claim that the population standard deviation is different from 60. (a) What is the level of significance? State the null and alternate hypotheses. Ho: a = 60; H₁: or <60 Ho: o = 60; H: σ #60 60 (b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) What are the degrees of freedom? Ho: o>60; H₁: a = 60 Ho: a = 60; H₁: o> What assumptions are you making about the original distribution? We assume a uniform population distribution. We assume a binomial population distribution. We assume a normal population distribution. We assume a exponential population distribution. (c) Find or estimate the P-value of the sample test statistic. P-value > 0.100 0.050 < P-value < 0.100 0.005 < P-value < 0.010 P-value < 0.005 0.025 < P-value < 0.050 0.010< P-value < 0.025

A factor in determining the usefulness of an examination as a measure of demonstrated ability is the amount of spread that occurs in the grades. If the spread or variation of examination scores is very small, it usually means that the examination was either too hard or too easy. However, if the variance of scores is moderately large, then there is a definite difference in scores between "better," "average," and "poorer" students. A group of attorneys in a midwestern state has been given the task of making up this year's bar examination for the state. The examination has 500 total possible points, and from the history of past examinations, it is known that a standard deviation of around 60 points is desirable. Of course, too large or too small a standard deviation is not good. The attorneys want to test their examination to see how good it is. A preliminary version of the examination (with slight modifications to protect the integrity of the real examination) is given to a random sample of 20 newly graduated law students. Their scores give a sample standard deviation of 73 points. Using a 0.01 level of significance, test the claim that the population standard deviation for the new examination is 60 against the claim that the population standard deviation is different from 60. (a) What is the level of significance? State the null and alternate hypotheses. Ho: a = 60; H₁: or <60 Ho: o = 60; H: σ #60 60 (b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) What are the degrees of freedom? Ho: o>60; H₁: a = 60 Ho: a = 60; H₁: o> What assumptions are you making about the original distribution? We assume a uniform population distribution. We assume a binomial population distribution. We assume a normal population distribution. We assume a exponential population distribution. (c) Find or estimate the P-value of the sample test statistic. P-value > 0.100 0.050 < P-value < 0.100 0.005 < P-value < 0.010 P-value < 0.005 0.025 < P-value < 0.050 0.010< P-value < 0.025

MATLAB: An Introduction with Applications
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 factor in determining the usefulness of an examination as a measure of demonstrated ability is the amount of spread that occurs in the grades. If the spread or variation of examination scores is very small, it usually means that the examination was either too hard or too easy. However, if the variance of scores s moderately large, then there is a definite difference in scores between "better," "average," and "poorer" students. A group of attorneys in a midwestern state has been given the task of making up this year's bar examination for the state. The examination has 500 total possible points, and from the history of past examinations, it is known that a standard deviation of around 60 points is desirable. Of course, too large or too small a standard deviation is not good. The attorneys want to test their examination to see how good it is. A preliminary version of the examination (with slight modifications to protect the integrity of the real examination) is given to a random sample of 20 newly graduated law students. Their scores give a sample standard deviation of 73 points. Using a 0.01 level of significance, test the claim that the population standard deviation for the new examination is 60 against the claim that the population standard deviation is different from 60. (a) What is the level of significance? State the null and alternate hypotheses. Ho: a = 60; Hig <60 Ho: g = 60; H: Ơ # 60 60 Ho: o>60; H: o = 600 Ho: o = 60; H₁: 0 > (b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) What are the degrees of freedom? What assumptions are you making about the original distribution? We assume a uniform population distribution. We assume a binomial population distribution. We assume a normal population distribution. We assume a exponential population distribution. (c) Find or estimate the P-value of the sample test statistic. P-value > 0.100 0.050 < P-value < 0.100 0.005< P-value < 0.010 P-value < 0.005 0.025 < P-value < 0.050 0.010 < P-value < 0.025 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Since the P-value > a, we fail to reject the null hypothesis. Since the P-value > x, we reject the null hypothesis. Since the P-values x, we reject the null hypothesis. to reject the null hypothesis. Since the P-values x, we fail (e) Interpret your conclusion in the context of the application. At the 1% level of significance, there is insufficient evidence to conclude that the standard deviation of test scores on the preliminary exam is different from 60. At the 1% level of significance, there is sufficient evidence to conclude that the standard deviation of test scores on the preliminary exam is different from 60.
Transcribed Image Text:A factor in determining the usefulness of an examination as a measure of demonstrated ability is the amount of spread that occurs in the grades. If the spread or variation of examination scores is very small, it usually means that the examination was either too hard or too easy. However, if the variance of scores s moderately large, then there is a definite difference in scores between "better," "average," and "poorer" students. A group of attorneys in a midwestern state has been given the task of making up this year's bar examination for the state. The examination has 500 total possible points, and from the history of past examinations, it is known that a standard deviation of around 60 points is desirable. Of course, too large or too small a standard deviation is not good. The attorneys want to test their examination to see how good it is. A preliminary version of the examination (with slight modifications to protect the integrity of the real examination) is given to a random sample of 20 newly graduated law students. Their scores give a sample standard deviation of 73 points. Using a 0.01 level of significance, test the claim that the population standard deviation for the new examination is 60 against the claim that the population standard deviation is different from 60. (a) What is the level of significance? State the null and alternate hypotheses. Ho: a = 60; Hig <60 Ho: g = 60; H: Ơ # 60 60 Ho: o>60; H: o = 600 Ho: o = 60; H₁: 0 > (b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) What are the degrees of freedom? What assumptions are you making about the original distribution? We assume a uniform population distribution. We assume a binomial population distribution. We assume a normal population distribution. We assume a exponential population distribution. (c) Find or estimate the P-value of the sample test statistic. P-value > 0.100 0.050 < P-value < 0.100 0.005< P-value < 0.010 P-value < 0.005 0.025 < P-value < 0.050 0.010 < P-value < 0.025 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Since the P-value > a, we fail to reject the null hypothesis. Since the P-value > x, we reject the null hypothesis. Since the P-values x, we reject the null hypothesis. to reject the null hypothesis. Since the P-values x, we fail (e) Interpret your conclusion in the context of the application. At the 1% level of significance, there is insufficient evidence to conclude that the standard deviation of test scores on the preliminary exam is different from 60. At the 1% level of significance, there is sufficient evidence to conclude that the standard deviation of test scores on the preliminary exam is different from 60.
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