5. (15 points) A random sample is drawn from a normal distribution:
3.5, 6.7, 2.0, 7.2, 4.8, 5.3, 6.7, 7.5, 6.4, 3.4
(a) Find the sample mean
(b) Find the standard error of sample mean
(c) If we would like to test whether the true mean is 6 or not,
i. state your null and alternative hypotheses
ii. compute the value of your test statistic
iii. compute the P-value
iv. If the significance level is chosen to be 0.01, then should your null hypothesis be rejected?