A sample of 16 elements is selected from a population with a reasonably symmetrical distribution. The sample mean is 100 and the sample standard deviation is 40. We can say that we are 90% confident that is between what two numbers? 12. What is the upper number? Maintain three decimal points in your calculations and give at least two decimal points in your answer.

We can say that we are 90% confident that the population mean is between 29.876 and 170.124.

The upper number is 170.124.

Step-by-step explanation:

We have the sample's standard deviation, so we use the students' t-distribution 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 = 16 - 1 = 15

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 15 degrees of freedom(y-axis) and a confidence level of ). So we have T = 1.7531

The margin of error is:

M = T*s = 40*1.7531 =70.124

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 100 - 70.124 = 29.876

The upper end of the interval is the sample mean added to M. So it is 100 + 70.124 = 170.124

We can say that we are 90% confident that the population mean is between 29.876 and 170.124.

The upper number is 170.124.

answ5

step-by-step explanation:

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