An article reported that 32% of college freshmen and 46% of college seniors carry a credit card balance from month to month. Suppose that the reported percentages were based on random samples of 1000 college freshmen and 1000 college seniors. (a) Construct a 90% confidence interval for the proportion of college freshmen who carry a credit card balance from month to month. (Round your answers to three decimal places.) (b) Construct a 90% confidence interval for the proportion of college seniors who carry a credit card balance from month to month. (Round your answers to three decimal places.) (c) Explain why the two 90% confidence intervals from parts (a) and (b) are not the same width. The widths of the two confidence intervals are different because the values of the estimated standard deviations of the sampling distributions of p are different. The widths of the two confidence intervals are different because the sample size n is large relative to the population size. The widths of the two confidence intervals are different because the sample size n is is small relative to the population size. The widths of the two confidence intervals are different because the z critical values used to calculate the confidence intervals are different.
An article reported that 32% of college freshmen and 46% of college seniors carry a credit card balance from month to month. Suppose that the reported percentages were based on random samples of 1000 college freshmen and 1000 college seniors. (a) Construct a 90% confidence interval for the proportion of college freshmen who carry a credit card balance from month to month. (Round your answers to three decimal places.) (b) Construct a 90% confidence interval for the proportion of college seniors who carry a credit card balance from month to month. (Round your answers to three decimal places.) (c) Explain why the two 90% confidence intervals from parts (a) and (b) are not the same width. The widths of the two confidence intervals are different because the values of the estimated standard deviations of the sampling distributions of p are different. The widths of the two confidence intervals are different because the sample size n is large relative to the population size. The widths of the two confidence intervals are different because the sample size n is is small relative to the population size. The widths of the two confidence intervals are different because the z critical values used to calculate the confidence intervals are different.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 1GP
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9.2.3
Transcribed Image Text:An article reported that 32% of college freshmen and 46% of college seniors carry a credit card balance from month to month. Suppose that the reported percentages were based on
random samples of 1000 college freshmen and 1000 college seniors.
(a) Construct a 90% confidence interval for the proportion of college freshmen who carry a credit card balance from month to month. (Round your answers to three decimal places.)
(b) Construct a 90% confidence interval for the proportion of college seniors who carry a credit card balance from month to month. (Round your answers to three decimal places.)
(c) Explain why the two 90% confidence intervals from parts (a) and (b) are not the same width.
The widths of the two confidence intervals are different because the values of the estimated standard deviations of the sampling distributions of p are different.
The widths of the two confidence intervals are different because the sample size n is large relative to the population size.
The widths of the two confidence intervals are different because the sample size n is is small relative to the population size.
The widths of the two confidence intervals are different because the z critical values used to calculate the confidence intervals are different.
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VIEWStep 4: Determine the reason two 90% confidence intervals from parts(a) and (b) are not the same width
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