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 ($) in the previous trip were recorded as follow: 8200 8500 4300 5200 5600 7800 2310 10000 It is assumed that
A, A surveying company wants to know the average amount of people spent in a trip. A random sample of 8 people was taken and their amount of spendings ($) in the previous trip were recorded as follow:
8200 8500 4300 5200 5600 7800 2310 10000 It is assumed that the amount spent was
-
(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?
B, 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 |
|
<4 |
0 |
|
5 |
2 |
|
6 |
5 |
|
7 |
15 |
|
8 |
10 |
|
9 |
3 |
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).)
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