Question 3.

Consider the sample below, which has been sampled from a normal distribution.

14.6, 15, 13.2, 15.5, 13.3, 8.8, 9.3, 10.9

Let n denote the sample size, let ˆµ denote the sample mean, let SE denote the standard error, and let µ denote the true population mean. Suppose you were testing the hypothesis

H0 : µ = 14 versus H1 : µ ̸= 14.

Assume a 5% level of significance.

(a) State the value of n, and determine ˆµ and SE.

(b) Using a t-distribution, calculate a 95% confidence interval for µ. Use R to find the appropriate value of tn−1,p.

(c) Based on your answer to (b), state an appropriate conclusion, with justification.

(d) Calculate the test statistic needed to perform a t-test for the hypotheses above.

(e) Use R to calculate the p-value for the t-test. You must clearly indicate the probability distribution(s) used.

(f) Based on your answer to (e), state an appropriate conclusion, with justification.

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