Use the standard normal distribution or the t-distribution to construct a 95% co

Question

Use the standard normal distribution or the t-distribution to construct a 95% confidence interval for the population mean. Justify your decision. If neither distribution can beused, explain why. Interpret the results.

In a recent season, the population standard deviation of the yards per carry for all running backs was 1.21. The yards per carry of 25 randomly selected running backs are shown below. Assume the yards per carry are normally distributed.

1.6        4.4        5.5        6.9        3.8        6.8        6.5        6.3        6.8        2.6        2.3        5.1        5.8
4.4        6.8        4.7        7.3        2.6        3.6        4.6        6.8        7.1        6.2        6.3        3.4

Which distribution should be used to construct the confidence interval?

A.Use a t-distribution because n<30 and is known.
B.Use a normal distribution because is known and the data are normally distributed.
C.Use a normal distribution because n<30, the miles per gallon are normally distributed and is unknown.
D.Use a t-distribution because n<30 and is unknown.
E.Cannot use the standard normal distribution or the t-distribution because is unknown, n<30, and the yards are not normally distributed.

Explanation / Answer

The given data follows normal distribution. Population standard deviation is known, and sample standard deviation and sample mean can be computed from the data. Therefore, with small sample, n<30, use a t distribution.

Option A)

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