Confidence intervals, hypothesis testing etc.

May 2010
Here r some Statistics Questions. Can someone help me to answer them?

1. Suppose a sample of n = 25 items is drawn from a population described
by a Normal distribution with standard deviation σ = 16, and that the
sample mean of the 25 values is 96.4. Derive a 95% confidence interval
for μ, the (unknown) mean of this distribution, and use your confidence
interval to test, at the 5% significance level, the hypothesis H0 : μ = 100
against the general (two-sided) alternative H1 : μ = 100.

2. Outline the changes to all calculations in Q1 if, instead of knowing
σ = 16, we have to estimate this quantity from the sample data, and
our estimate is
s = 17.
Repeat the test of the hypothesis in Q1, and decide whether your conclusions
change in these circumstances.

3. Illustrate the p-values for the above hypothesis (with σ known or not),
using sketches based on the appropriate reference distribution. Calculate
the p-values associated with the tests outlined in Q1 and Q2.
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