A random sample of 25 values is drawn from a mound-shaped and symmetrical distribution. The sample mean is 10 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 9.5.

(a) Is it appropriate to use a Student's t distribution? Explain. How many degrees of freedom do we use?
(b) What are the hypotheses?
(c) Compute the sample test statistic t.
(d) Estimate the P-value for the test.
(e) Do we reject or fail to reject H_0?
(f) Interpret the results.

Given that random sample of 25 values is drawn from a mound-shaped and symmetrical distribution. The sample mean is 10 and the sample standard deviation is 2.

95 % CI for mean 9.1744 to 10.8256

Since p >0.05 accept null hypothesis.

a) Yes because std dev sigma not known. df = 24

b)

H0: x bar = 9.5

Ha: x bar not equals 9.5

c) t-statistic 1.250

d) P = 0.2234

e) We fail to reject null hypothesis

f) There is no statistical evidence at 5% level to fail to reject H0.