help with stats hw

Question

A simple random sample of size n is drawn. The sample​ mean,

x is found to be 18.6​,

and the sample standard​ deviation, s, is found to be

4.6.

Click the icon to view the table of areas under the​ t-distribution.

​(a) Construct a

95​%

confidence interval about

muμ

if the sample​ size, n, is

35

Lower​ bound: ____

Upper​ bound: ____

​(Use ascending order. Round to two decimal places as​ needed.)

Answer 1

If the sample size is 35, the degrees of freedom for the t distribution is 34, but since the table only shows values for 30 and 40 degrees of freedom, we will select the critical t value for 30 degrees of freedom that corresponds to a 95% confidence interval (0.025 tail value), which is 2.042.

The 95% confidence interval is equal to sample mean +/- t critical value * sample standard deviation/sample size^0.5 (the part after the +/- sign is called the margin of error)

The sample mean = 18.6, the sample standard deviation is 4.6, the t critical value is 2.042 and the sample size is 35, so you just need to plug in those numbers to get the lower and upper limits (sample mean - margin of error, sample mean + margin of error).