In a random sample of people, the mean driving distance to work was miles and the standard deviation was miles. Assume the population is normally distributed and use the t-distribution to find the margin of error and construct a % confidence interval for the population mean . Interpret the results. Identify the margin of error.

Complete  Question

In a random sample of  ten  people, the mean driving distance to work was  23.1 miles and the standard deviation was  6.6 miles. Assume the population is normally distributed and use the t-distribution to find the margin of error and construct a  99%  confidence interval for the population mean Interpret the results.  Identify the margin of error.

The  99% confidence interval is  

The interpretation is that there is 99% confidence that the true mean lies within the limits

The margin of error is  

Step-by-step explanation:

From the question we are told that

   The sample mean is  

     The standard deviation is  

    The  sample size is  n = 10

Generally the degree of freedom is mathematically represented as

=>  

=>  

Given that the confidence level is 99% , the n the level of significance is mathematically evaluated as

Next we obtain the critical value of   with a df of  9  from from the student t-distribution table the value is  

Generally the margin of error is mathematically represented as

The 99% confidence interval is

=>  

=>  

The interpretation is that there is 99% confidence that the true mean lies within the limits

answer4 to the second power is 16

and 4 to the third power is 64,