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A sample of 40 country CD recordings of Willie Nelson has been examined. The average playing time of these recordings is 51.3 minutes, and the standard deviation is s = 5.8 minutes. Using an appropriate t-multiplier, construct a 95% confidence interval for the mean playing time of all Willie Nelson recordings. Place your LOWER limit, in minutes, rounded to 2 decimal places, in the first blank. For example, 56.78 would be a legitimate entry.___. Place your UPPER limit, in minutes, rounded to 2 decimal places, in the second blank. For example, 67.89 would be a legitimate entry.___

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Answer:

Lower limit: 49.44 minutes

Upper limit: 53.16 minutes

Step-by-step explanation:

T interval

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 40 - 1 = 39

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 39 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.023

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.023\frac{5.8}{\sqrt{40}} = 1.86[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 51.3 - 1.86 = 49.44 minutes

The upper end of the interval is the sample mean added to M. So it is 51.3 + 1.86 = 53.16 minutes

Lower limit: 49.44 minutes

Upper limit: 53.16 minutes

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