Every year, all incoming high school freshmen in a large school district take a math placement test. For this year's test, the district has prepared two possible versions: Version 1 that covers more material than last year's test and Version 2 test that is similar to last year's test. The district suspects that the mean score for Version 1 will be less than the mean score for Version 2. To examine this, over the summer the district randomly selects 60 incoming freshmen to come to its offices to take Version 1, and it randomly selects 70 incoming freshmen to come take Version 2. The 60 incoming freshmen taking Version 1 score a mean of 112.3 points with a standard deviation of 13.4. The 70 incoming freshmen taking Version 2 score a mean of 117.7 points with a standard deviation of 16.8. Assume that the population standard deviations of the test scores from the two versions can be estimated to be the sample standard deviations, since the samples that are used to compute them are quite large. At the 0.05 level of significance, is there enough evidence to support the claim that the mean test score, u,, for Version 1 is less than the mean test score, u,, for Version 2? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H, - H, :0 H, :0 OP (b) Determine the type of test statistic to use. (Choose one) ▼ D=0 OSO (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) (e) Can we support the claim that the mean test score for Version 1 is less than the mean test score of Version 2? O Yes ONo a
Every year, all incoming high school freshmen in a large school district take a math placement test. For this year's test, the district has prepared two possible versions: Version 1 that covers more material than last year's test and Version 2 test that is similar to last year's test. The district suspects that the mean score for Version 1 will be less than the mean score for Version 2. To examine this, over the summer the district randomly selects 60 incoming freshmen to come to its offices to take Version 1, and it randomly selects 70 incoming freshmen to come take Version 2. The 60 incoming freshmen taking Version 1 score a mean of 112.3 points with a standard deviation of 13.4. The 70 incoming freshmen taking Version 2 score a mean of 117.7 points with a standard deviation of 16.8. Assume that the population standard deviations of the test scores from the two versions can be estimated to be the sample standard deviations, since the samples that are used to compute them are quite large. At the 0.05 level of significance, is there enough evidence to support the claim that the mean test score, u,, for Version 1 is less than the mean test score, u,, for Version 2? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H, - H, :0 H, :0 OP (b) Determine the type of test statistic to use. (Choose one) ▼ D=0 OSO (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) (e) Can we support the claim that the mean test score for Version 1 is less than the mean test score of Version 2? O Yes ONo a
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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![Every year, all incoming high school freshmen in a large school district take a math placement test. For this year’s test, the district has prepared two possible versions: Version 1 that covers more material than last year’s test and Version 2 that is similar to last year’s test. The district suspects that the mean score for Version 1 will be less than the mean score for Version 2. To examine this, over the summer the district randomly selects 60 incoming freshmen to come to its offices to take Version 1, and it randomly selects 70 incoming freshmen to come take Version 2. The 60 incoming freshmen taking Version 1 score a mean of 112.3 points with a standard deviation of 13.4. The 70 incoming freshmen taking Version 2 score a mean of 117.7 points with a standard deviation of 16.8. Assume that the population standard deviations of the test scores from the two versions can be estimated to be the sample standard deviations, since the samples that are used to compute them are quite large. At the 0.05 level of significance, is there enough evidence to support the claim that the mean test score, μ₁, for Version 1 is less than the mean test score, μ₂, for Version 2? Perform a one-tailed test. Then complete the parts below.
Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.)
(a) State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \).
\( H_0 \): [ ]
\( H_1 \): [ ]
(b) Determine the type of test statistic to use.
(Choose one)
[ ]
(c) Find the value of the test statistic. (Round to three or more decimal places.)
[ ]
(d) Find the p-value. (Round to three or more decimal places.)
[ ]
(e) Can we support the claim that the mean test score for Version 1 is less than the mean test score of Version 2?
Yes [ ] No [ ]
On the right side of the screen, there is a toolbar with options for various statistical symbols and operations, including symbols for mean (\( \mu \)), standard deviation (\( \sigma \)), and others relevant to hypothesis testing and statistical analysis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Febcf9de3-24cc-40b0-a023-15a9096e4963%2Fb6f650a6-92b2-4261-aadb-4e85a17e5241%2Far00nx3_processed.png&w=3840&q=75)
Transcribed Image Text:Every year, all incoming high school freshmen in a large school district take a math placement test. For this year’s test, the district has prepared two possible versions: Version 1 that covers more material than last year’s test and Version 2 that is similar to last year’s test. The district suspects that the mean score for Version 1 will be less than the mean score for Version 2. To examine this, over the summer the district randomly selects 60 incoming freshmen to come to its offices to take Version 1, and it randomly selects 70 incoming freshmen to come take Version 2. The 60 incoming freshmen taking Version 1 score a mean of 112.3 points with a standard deviation of 13.4. The 70 incoming freshmen taking Version 2 score a mean of 117.7 points with a standard deviation of 16.8. Assume that the population standard deviations of the test scores from the two versions can be estimated to be the sample standard deviations, since the samples that are used to compute them are quite large. At the 0.05 level of significance, is there enough evidence to support the claim that the mean test score, μ₁, for Version 1 is less than the mean test score, μ₂, for Version 2? Perform a one-tailed test. Then complete the parts below.
Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.)
(a) State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \).
\( H_0 \): [ ]
\( H_1 \): [ ]
(b) Determine the type of test statistic to use.
(Choose one)
[ ]
(c) Find the value of the test statistic. (Round to three or more decimal places.)
[ ]
(d) Find the p-value. (Round to three or more decimal places.)
[ ]
(e) Can we support the claim that the mean test score for Version 1 is less than the mean test score of Version 2?
Yes [ ] No [ ]
On the right side of the screen, there is a toolbar with options for various statistical symbols and operations, including symbols for mean (\( \mu \)), standard deviation (\( \sigma \)), and others relevant to hypothesis testing and statistical analysis.
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