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a. Suppose that a random sample of 41 state college students is asked to measure the length of their right foot in centimeters. A 95% confidence interval for the mean foot length for students at this university turns out to be (21.709, 25.091). If we now calculated a 90% confidence interval, would the new confidence interval be wider than or narrower than or the same as the original? b. Suppose two researchers want to estimate the proportion of American college students who favor abolishing the penny. They both want to have about the same margin of error to estimate this proportion. However, Researcher 1 wants to estimate with 95% confidence and Researcher 2 wants to estimate with 99% confidence. Which researcher would need fewer students for her study in order to obtain the desired margin of error? The answer is Researcher c. A 95% confidence interval for the mean reading achievement score for a population of third grade students is (55, 65). The margin of error of this interval is what whole number?

a. Suppose that a random sample of 41 state college students is asked to measure the length of their right foot in centimeters. A 95% confidence interval for the mean foot length for students at this university turns out to be (21.709, 25.091). If we now calculated a 90% confidence interval, would the new confidence interval be wider than or narrower than or the same as the original? b. Suppose two researchers want to estimate the proportion of American college students who favor abolishing the penny. They both want to have about the same margin of error to estimate this proportion. However, Researcher 1 wants to estimate with 95% confidence and Researcher 2 wants to estimate with 99% confidence. Which researcher would need fewer students for her study in order to obtain the desired margin of error? The answer is Researcher c. A 95% confidence interval for the mean reading achievement score for a population of third grade students is (55, 65). The margin of error of this interval is what whole number?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section: Chapter Questions
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a. Suppose that a random sample of 41 state college students is asked to measure the length of their right foot in centimeters. A 95% confidence interval for the mean foot length for students at this university turns out to be (21.709, 25.091). If we now calculated a 90% confidence interval, would the new confidence interval be wider than or narrower than or the same as the original? b. Suppose two researchers want to estimate the proportion of American college students who favor abolishing the penny. They both want to have about the same margin of error to estimate this proportion. However, Researcher 1 wants to estimate with 95% confidence and Researcher 2 wants to estimate with 99% confidence. Which researcher would need fewer students for her study in order to obtain the desired margin of error? The answer is Researcher c. A 95% confidence interval for the mean reading achievement score for a population of third grade students is (55, 65). The margin of error of this interval is what whole number? d. Two different samples will be taken from the same population of test scores where the population mean and standard deviation are unknown. The first sample will have 25 data values, and the second sample will have 64 data values. A 95% confidence interval will be constructed for each sample to estimate the population mean. Which number of data values would you expect to give a greater precision (a smaller width) for estimating the population mean? The answer is the sample with data values. e. Each of the 110 students in a statistics class selects a different random sample of 35 quiz scores from a population of 5000 quiz scores they are given. Using their data, each student constructs a 90% confidence interval for mu, the average quiz score of the 5000 students. Is the following statement correct, yes or no? About 10% of the raw scores in the samples will not be found in these confidence intervals.
Transcribed Image Text:a. Suppose that a random sample of 41 state college students is asked to measure the length of their right foot in centimeters. A 95% confidence interval for the mean foot length for students at this university turns out to be (21.709, 25.091). If we now calculated a 90% confidence interval, would the new confidence interval be wider than or narrower than or the same as the original? b. Suppose two researchers want to estimate the proportion of American college students who favor abolishing the penny. They both want to have about the same margin of error to estimate this proportion. However, Researcher 1 wants to estimate with 95% confidence and Researcher 2 wants to estimate with 99% confidence. Which researcher would need fewer students for her study in order to obtain the desired margin of error? The answer is Researcher c. A 95% confidence interval for the mean reading achievement score for a population of third grade students is (55, 65). The margin of error of this interval is what whole number? d. Two different samples will be taken from the same population of test scores where the population mean and standard deviation are unknown. The first sample will have 25 data values, and the second sample will have 64 data values. A 95% confidence interval will be constructed for each sample to estimate the population mean. Which number of data values would you expect to give a greater precision (a smaller width) for estimating the population mean? The answer is the sample with data values. e. Each of the 110 students in a statistics class selects a different random sample of 35 quiz scores from a population of 5000 quiz scores they are given. Using their data, each student constructs a 90% confidence interval for mu, the average quiz score of the 5000 students. Is the following statement correct, yes or no? About 10% of the raw scores in the samples will not be found in these confidence intervals.
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