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Question | (10 marks) A surveying company wants to know the average amount of people spent in a trip

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Question | (10 marks)

A surveying company wants to know the average amount of people spent in a trip. A random sample of 8

people was taken and their amount of spendings ($) in the previous trip were recorded as follow:

8200 8500 4300 5200 5600 7800 2310 10000

It is assumed that the amount spent was normally distributed.

(a) Construct a 95% confidence interval of the population mean spending in a trip.

(b) If the similar survey would be done regularly, each time with the same sample size n = 8. After the
construction of 50 confidence intervals, each at 95% confidence level, approximately how many such
intervals can successfully include the unknown population mean?

Question 2 (20 marks)

A tutorial school has been running IELTS mock examination for many years. Below is the summary

presented by the tutorial school related to the IELTS mock examination in one of the many online classes

selected randomly in year 2022.

IELTS score in mock examination | Number of students
es ee ee
PS

(c) Ifthe confidence interval estimate in part (a) 1s constructed at 99% instead of 95%, would the interval be
(1) wider, (II) narrower, or (II]) no change in width? (State your answer, no explanation is needed in
part (c).)
a
0 -
The entries in Table I are the probabilities that a random variable having the
standard normal distribution will take on a value between 0 andz. They are given
by the area of the gray region under the curve in the figure.
TABLE I NORMAL-CURVE AREAS
z 0.00 0.01 0.02 0.03 0. 0.05 0.06 0.07 0.08 0.09
0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359
fy 1 Ly NOOO fV, NAIDOO Lf (QHATIO fy O17 VY NVLEO7 LY ALOL fY NLIL fV AL 7S f\ NILA HY nn 7zo49

Question 2 (20 marks)
A tutorial school has been running IELTS mock examination for many years. Below 1s the summary
presented by the tutorial school related to the IELTS mock examination in one of the many online classes
selected randomly in year 2022.
po
a ee ee
ot
a ee ee
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 (1) null hypothesis and alternative hypothesis,
(11) rejection region(s), (111) calculation of test PETIA cs and (iv) conclusion.)