First we need the hypotheses:

Ho: Mu = 10

Ha: Mu > 10

now get the test statistic t, since sample size is small and population standard deviation is not known.

t = (x-bar - Mu)/(standard deviation/square root(n))

t = (9.5 - 10)/(2.5/square root(16))

t = -0.8

We get the critical value for the test,

look up t at n-1 df for one tailed area of .05

t, 15df, .05 = 1.753

Since -0.8 < 1.753, we do not reject Ho. There is not enough evidence to support the claim that mean is greater than 10

For part b, the CI is x-bar+/- t(standard deviation/square root(n))

t for 95% interval, 15 df is 2.131

CI = 9.5 +/- 2.131(2.5/sqrt(16)) = 9.5 +/- 1.332

(8.168, 10.832)

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