A student claims that the population mean of weight of HKUST students is NOT 58kg. A random sample of 16 students are tested and the sample mean is 60kg. Assume the weight is normally distributed with the population standard deviation as 3.3kg. We will do a hypothesis testing at 1% level of significance to test the claim.
a. Set up the null hypothesis and alternative hypothesis.
b. Which test should we use: Upper-tail test? Or Lower-tail test? Or Two-sided test?
c. Which test should we use: z-test or t-test or Chi-square test? Find the value of the corresponding statistic (i.e., the z-statistic, or t-statistic, or the Chi-square statistic)
d. Find the p-value.
e. Should we reject the null hypothesis? Use the result of (d) to explain the reason.
f. What is the conclusion based on (e)?
g. Can we use confidence interval for the population mean of weight of HKUST students to test the hypothesis in (a)? If yes, which confidence interval should we use to reach the same decision in (e)? If no, why?