A College wished to know the number of library books borrowed by students over a term. 16 students were selected at random and the following data were obtained for the books they borrowed:
24, 22, 25, 25, 21, 26, 27, 22, 24, 23, 28, 23, 28, 25, 26, 21
(i) Calculate a 95% confidence interval for the population mean, .
(ii) Calculate a 95% confidence interval for the population variance.
(iii) Show that for any claimed value of the U for the Uo inside the 95% confidence interval, a test of the hypothesis Ho: u = uo against the alternative H1: u =/=uo would not lead to the rejection of Ho for alpha = 0.05.
This solution calculates the sample mean and test statistic to compare it against the confidence interval. The same is done with population variation and also a hypothesis test is conducted to accept or reject the null hypothesis.