2-sided alternative hypothesis

Assuming the rest of my work is correct for this question, I am having trouble on part c. I don't know if I have the right formula and, if I do, I don't know how to calculate .

Let X equal the length of wood blocks manufactured. Assume distribution of X is . The greatest lenth is 7.5 inches. We shall test the null hypothesis against a 2-sided alternative hypothesis using 10 observations.

a) Define test statistic and critical region for an significance level.

test statistic-

critical region-

Calculate the value of the test statistic and give your decision using the following data (n=10)

7.65

7.60

7.65

7.70

7.55

7.55

7.40

7.40

7.50

7.50

s=0.10274

t=1.539

1.539 is not greater than 2.262, therefore, it fails to reject

c) Is contained in a 95% confidence interval for ?

As of now, I am using my values of , s=0.10274 and n=10

Thank you for helping!