Use the standard normal distribution or the t-distribution to construct a 90% confidence interval for the population mean. Justify your decision. If neither distributior can be used, explain why. Interpret the results. In a recent season, the population standard deviation of the yards per carry for all running backs was 1.29. The yards per carry of 25 randomly selected running backs are shown below. Assume the yards per carry are normally distributed. 1.6 5.4 2.7 2.5 6.8 5.3 3.8 4.7 4.4 3.8 2.6 2.2 2.6 5.6 2.5 4.7 5.6 3.6 3.5 5.9 3.9 4.4 4.4 4.6 4.2 Which distribution should be used to construct the confidence interval? ...... A. Use a normal distribution because o is known and the data are normally distributed. O B. Use a t-distribution because n< 30 and o is known. O C. Use a normal distribution because n<30, the data are normally distributed and o is unknown. O D. Use a t-distribution because n< 30 and o is unknown. O E. Cannot use the standard normal distribution or the t-distribution because o is unknown, n< 30, and the data are not normally distributed. Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice. O A. The 90% confidence interval is ( ). (Round to two decimal places as needed.) O B. Neither distribution can be used to construct the confidence interval.
Use the standard normal distribution or the t-distribution to construct a 90% confidence interval for the population mean. Justify your decision. If neither distributior can be used, explain why. Interpret the results. In a recent season, the population standard deviation of the yards per carry for all running backs was 1.29. The yards per carry of 25 randomly selected running backs are shown below. Assume the yards per carry are normally distributed. 1.6 5.4 2.7 2.5 6.8 5.3 3.8 4.7 4.4 3.8 2.6 2.2 2.6 5.6 2.5 4.7 5.6 3.6 3.5 5.9 3.9 4.4 4.4 4.6 4.2 Which distribution should be used to construct the confidence interval? ...... A. Use a normal distribution because o is known and the data are normally distributed. O B. Use a t-distribution because n< 30 and o is known. O C. Use a normal distribution because n<30, the data are normally distributed and o is unknown. O D. Use a t-distribution because n< 30 and o is unknown. O E. Cannot use the standard normal distribution or the t-distribution because o is unknown, n< 30, and the data are not normally distributed. Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice. O A. The 90% confidence interval is ( ). (Round to two decimal places as needed.) O B. Neither distribution can be used to construct the confidence interval.
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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Transcribed Image Text:Use the standard normal distribution or the t-distribution to construct a 90% confidence interval for the population mean. Justify your decision. If neither distribution
can be used, explain why. Interpret the results.
In a recent season, the population standard deviation of the yards per carry for all running backs was 1.29. The yards per carry of 25 randomly selected running
backs are shown below. Assume the yards per carry are normally distributed.
5.4
5.6
1.6
2.7
2.5
6.8
5.3
3.8
4.7
4.4
3.8
2.2
2.6
5.6
2.5
4.7
3.6
3.5
5.9
3.9
44
2.6
4.4
4.6
4.2
Which distribution should be used to construct the confidence interval?
A. Use a normal distribution because o is known and the data are normally distributed.
O B. Use a t-distribution because n<30 and o is known.
O C. Use a normal distribution because n<30, the data are normally distributed and o is unknown.
O D. Use a t-distribution because n< 30 and o is unknown.
O E. Cannot use the standard normal distribution or the t-distribution because o is unknown, n< 30, and the data are not normally distributed.
Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice.
O A. The 90% confidence interval is ( ).
(Round to two decimal places as needed.)
O B. Neither distribution can be used to construct the confidence interval.
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