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The weights of running shoes are normally distributed with an unknown population mean and standard deviation. If a random sample of 23 running shoes is taken and results in a sample mean of 12 ounces and sample standard deviation of 3 ounces, find the margin of error, ME, for a 95% confidence interval estimate for the population mean using the Student's t-distribution.

Respuesta :

Answer:

The margin of error for a 95% confidence interval estimate for the population mean using the Student's t-distribution is of 6.22 ounces.

Step-by-step explanation:

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 = 23 - 1 = 22

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 22 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0739

The margin of error is:

M = T*s

In which s is the standard deviation of the sample.

In this question:

s = 3.

Then

M = 2.0739*3 = 6.22

The margin of error for a 95% confidence interval estimate for the population mean using the Student's t-distribution is of 6.22 ounces.

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