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Answer:
The 90% confidence interval estimate of the mean of the population is between 6627 and 6941.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
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 = 15 - 1 = 14
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of . So we have T = 1.761
The margin of error is:
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 6784 - 157 = 6627
The upper end of the interval is the sample mean added to M. So it is 6784 + 157 = 6941
The 90% confidence interval estimate of the mean of the population is between 6627 and 6941.