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Math Statistics OPENINTRO:STATISTICS

(a) To interpret : 95% confidence for population mean number of hours. Given information: Sample size ( n ) = 1155 Confidence level = 95 % Confidence interval ( 1.38 , 1.92 ) Concept used: Confidence interval can be rewritten as Mean - Margin of error , Mean + Margin of error Margin of Error can be written as E=critical value× standard deviation sample size Interpretation: With 95% confidence, it can be said that the true population mean number of hours spent on relaxing or pursuing activities they enjoy lies between ( 0.5661 , 0.6339 ) . If 100 confidence intervals are conducted with same sample size, then 95 of them will include the true population mean number of hours. (b) To compare: The confidence interval when margin of error is increased. The confidence interval widens when margin of error increases. There is a direct relationship between the width of a confidence interval and margin of error. So, if the margin of error is increased then width of the confidence interval also increases. So, the confidence interval with the higher margin of error would be wider because larger margin of error widens the confidence interval. (c) To compare: The margin of error if the sample size is increased. The margin of error decreases when the sample size is 2500 From the formula of margin of error stated above, it can be seen that sample size in inversely proportional to margin of error. This means that if sample size increases, margin of error decreases and vice versa. Thus, the margin of error will decrease when the sample size is increased to 2500 keeping other factors constant.

(a) To interpret : 95% confidence for population mean number of hours. Given information: Sample size ( n ) = 1155 Confidence level = 95 % Confidence interval ( 1.38 , 1.92 ) Concept used: Confidence interval can be rewritten as Mean - Margin of error , Mean + Margin of error Margin of Error can be written as E=critical value× standard deviation sample size Interpretation: With 95% confidence, it can be said that the true population mean number of hours spent on relaxing or pursuing activities they enjoy lies between ( 0.5661 , 0.6339 ) . If 100 confidence intervals are conducted with same sample size, then 95 of them will include the true population mean number of hours. (b) To compare: The confidence interval when margin of error is increased. The confidence interval widens when margin of error increases. There is a direct relationship between the width of a confidence interval and margin of error. So, if the margin of error is increased then width of the confidence interval also increases. So, the confidence interval with the higher margin of error would be wider because larger margin of error widens the confidence interval. (c) To compare: The margin of error if the sample size is increased. The margin of error decreases when the sample size is 2500 From the formula of margin of error stated above, it can be seen that sample size in inversely proportional to margin of error. This means that if sample size increases, margin of error decreases and vice versa. Thus, the margin of error will decrease when the sample size is increased to 2500 keeping other factors constant.

Solution Summary: The author explains that 95% confidence for population mean number of hours lies between (0.5661,0.6339) and margin of error.

OPENINTRO:STATISTICS

OPENINTRO:STATISTICS

4th Edition

ISBN: 9781943450077

Author: OPENINTRO

Publisher: amazon.com

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A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

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Chapter 5.3, Problem 26E

Chapter 5, Problem 28CE

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OPENINTRO:STATISTICS

Ch. 5.3 - Prob. 25GP Ch. 5 - Prob. 27CE Ch. 5 - Prob. 32CE

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