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(a) Why are we allowed to assume that the sampling distribution in this problem is approximately normal? O The margin of error is unknown. The population standard deviation is known. The population is normally distributed. The sample size is large enough. (b) Which distribution should be used to find the critical value? O The t-distribution because o is unknown. The t-distribution because the sample size is small. The Z-distribution because o is known. The z-distribution because the sample mean is large enough. (c) Construct a 90% confidence interval for the true average commute time. Round your answers to two decimal places. lower limit upper limit margin of error

(a) Why are we allowed to assume that the sampling distribution in this problem is approximately normal? O The margin of error is unknown. The population standard deviation is known. The population is normally distributed. The sample size is large enough. (b) Which distribution should be used to find the critical value? O The t-distribution because o is unknown. The t-distribution because the sample size is small. The Z-distribution because o is known. The z-distribution because the sample mean is large enough. (c) Construct a 90% confidence interval for the true average commute time. Round your answers to two decimal places. lower limit upper limit margin of error

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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A researcher wants to estimate the average time a person spends commuting to Boston. The researcher chooses a random sample of 22 people and finds that their average commute is 49 minutes with a standard deviation of 19 minutes. Assume that commute times are normally distributed. (a) Why are we allowed to assume that the sampling distribution in this problem is approximately normal? O The margin of error is unknown. O The population standard deviation is known. O The population is normally distributed. O The sample size is large enough. (b) Which distribution should be used to find the critical value? O The t-distribution because o is unknown. O The t-distribution because the sample size is small. O The Z-distribution because o is known. O The z-distribution because the sample mean is large enough. (c) Construct a 90% confidence interval for the true average commute time. Round your answers to two decimal places. lower limit upper limit margin of error
Transcribed Image Text:A researcher wants to estimate the average time a person spends commuting to Boston. The researcher chooses a random sample of 22 people and finds that their average commute is 49 minutes with a standard deviation of 19 minutes. Assume that commute times are normally distributed. (a) Why are we allowed to assume that the sampling distribution in this problem is approximately normal? O The margin of error is unknown. O The population standard deviation is known. O The population is normally distributed. O The sample size is large enough. (b) Which distribution should be used to find the critical value? O The t-distribution because o is unknown. O The t-distribution because the sample size is small. O The Z-distribution because o is known. O The z-distribution because the sample mean is large enough. (c) Construct a 90% confidence interval for the true average commute time. Round your answers to two decimal places. lower limit upper limit margin of error
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