Data on fifth-grade test scores (reading and mathematics) for 406 school districts in California yield Y = 633.3 and standard deviation sy = 19.1. The 95% confidence interval for the mean test score in the population is (631.44, 635.16). (Round your responses to two decimal places.) When the districts were divided into districts with small classes (< 20 students per teacher) and large classes (≥20 students per teacher), the following results were found: Class Size Small Large Average Score (Y) 644.3 637.0 Standard Deviation (sy) n 19.0 17.5 243 180 Is there statistically significant evidence that the districts with smaller classes have higher average test scores? The t-statistic for testing the null hypothesis is 4.09. (Round your response to two decimal places.) The p-value for the test is (Round your response to six decimal places.) Hint: Use the Excel function. Norm.S.Dist to help answer this question. In a survey of 400 likely voters, 214 responded that they would vote for the incumbent and 186 responded that they would vote for the challenger. Let p denote the fraction of all likely voters who preferred the incumbent at Α the time of the survey, and let p be the fraction of survey respondents who preferred the incumbent. Using the survey results, the estimated value of p is 0.5350. (Round your response to four decimal places.) ^ Using p(1 - p)/n as the estimator of the variance of p, the standard error of the estimator is 0.0249. (Round your response to four decimal places.) The p-value for the test Ho: p = 0.5 versus H₁: p 0.5 is 0.160. (Round your response to three decimal places.) The p-value for the test Ho: p = 0.5 versus H₁: p > 0.5 is (Round your response to three decimal places.)
Data on fifth-grade test scores (reading and mathematics) for 406 school districts in California yield Y = 633.3 and standard deviation sy = 19.1. The 95% confidence interval for the mean test score in the population is (631.44, 635.16). (Round your responses to two decimal places.) When the districts were divided into districts with small classes (< 20 students per teacher) and large classes (≥20 students per teacher), the following results were found: Class Size Small Large Average Score (Y) 644.3 637.0 Standard Deviation (sy) n 19.0 17.5 243 180 Is there statistically significant evidence that the districts with smaller classes have higher average test scores? The t-statistic for testing the null hypothesis is 4.09. (Round your response to two decimal places.) The p-value for the test is (Round your response to six decimal places.) Hint: Use the Excel function. Norm.S.Dist to help answer this question. In a survey of 400 likely voters, 214 responded that they would vote for the incumbent and 186 responded that they would vote for the challenger. Let p denote the fraction of all likely voters who preferred the incumbent at Α the time of the survey, and let p be the fraction of survey respondents who preferred the incumbent. Using the survey results, the estimated value of p is 0.5350. (Round your response to four decimal places.) ^ Using p(1 - p)/n as the estimator of the variance of p, the standard error of the estimator is 0.0249. (Round your response to four decimal places.) The p-value for the test Ho: p = 0.5 versus H₁: p 0.5 is 0.160. (Round your response to three decimal places.) The p-value for the test Ho: p = 0.5 versus H₁: p > 0.5 is (Round your response to three decimal places.)
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Data on fifth-grade test scores (reading and mathematics) for 406 school districts in California yield Y = 633.3
and standard deviation sy = 19.1.
The 95% confidence interval for the mean test score in the population is (631.44, 635.16). (Round your
responses to two decimal places.)
When the districts were divided into districts with small classes (< 20 students per teacher) and large classes
(≥20 students per teacher), the following results were found:
Class Size
Small
Large
Average Score (Y)
644.3
637.0
Standard Deviation (sy)
n
19.0
17.5
243
180
Is there statistically significant evidence that the districts with smaller classes have higher average test scores?
The t-statistic for testing the null hypothesis is 4.09. (Round your response to two decimal places.)
The p-value for the test is
(Round your response to six decimal places.) Hint: Use the Excel function.
Norm.S.Dist to help answer this question.
Transcribed Image Text:In a survey of 400 likely voters, 214 responded that they would vote for the incumbent and 186 responded that
they would vote for the challenger. Let p denote the fraction of all likely voters who preferred the incumbent at
Α
the time of the survey, and let p be the fraction of survey respondents who preferred the incumbent.
Using the survey results, the estimated value of p is 0.5350. (Round your response to four decimal places.)
^
Using p(1 - p)/n as the estimator of the variance of p, the standard error of the estimator is 0.0249. (Round
your response to four decimal places.)
The p-value for the test Ho: p = 0.5 versus H₁: p 0.5 is 0.160. (Round your response to three decimal
places.)
The p-value for the test Ho: p = 0.5 versus H₁: p > 0.5 is
(Round your response to three decimal places.)
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