A report presented by this tutorial school 5 years ago indicated that the population mean score of IELTS mock examination was 7.05 points and the population proportion of students got 7 points or...

 A report presented by this tutorial school 5 years ago indicated that the population mean score of IELTS mock examination was 7.05 points and the population proportion of students got 7 points or above was 0.67.

(a) Construct a 95% confidence interval estimate of population mean score a student get in the IELTS mock examination in 2022.

(b) Test, at 1% level of significance, if the population proportion of students get 7 points or above in 2022 is higher than that in year 2017. (The report must include the (i) null hypothesis and alternative hypothesis, (ii) rejection region(s), (iii) calculation of test statistics, and (iv) conclusion.)

(c) If the confidence interval estimate in part (a) is constructed at 99% instead of 95%, would the interval be (I) wider, (II) narrower, or (III) no change in width? (State your answer, no explanation is needed in part (c).)