ECON10071/20071 - 2023/24
Week 9 - Practice Exercises
Hypothesis Testing and Confidence Intervals
1. The YouGov Voting Intention opinion poll (for end of March 2023) delivers the following table of results to the question ”Which of the following do you think would make the best Prime Minister?”.
|
Obs Percentages
Prime Minister
|
Age 18-24
|
25-49
|
50-64
|
65+
|
|
Rishi Sunak
|
18%
|
19%
|
27%
|
42%
|
|
Keir Starmer
|
28%
|
34%
|
30%
|
25%
|
|
Not Sure
|
41%
|
42%
|
41%
|
31%
|
|
Refused
|
13%
|
5%
|
2%
|
2%
|
|
Total
|
100%
|
100%
|
100%
|
100%
|
Test whether the variables (preferred prime minister, P , and age, A) are independent.
2. In order to see whether their random sample has the same average age as the intended population (voting age population), YouGov wishes to calculate a confidence interval for the average age, µ, using a sample of n = 2003. Calculate a 99% confidence interval. The sample average age is 46.3 years. From excellent population data from the last census we know that the population variance in age is σ 2 = 90.
3. Using the same data, calculate a 95% confidence interval for the population percentage of Rishi Sunak and Keir Starmer supporters amongst the 19 to 24 year olds (separate confidence intervals for both party leaders).
Test whether the variables (preferred prime minister, P , and age, A) are independent.
|
Age
18-24 25-49 50-64 65+ Total
|
|
Total 210 827 495 471 2003
|
|
Obs number
Prime Minister(Pi )
|
Age(Aj ) 18-24
|
25-49
|
50-64
|
65+
|
Total
|
|
Rishi Sunak
|
38
|
157
|
|
198
|
|
|
Keir Starmer
|
59
|
|
149
|
118
|
|
|
Not Sure
|
86
|
347
|
203
|
146
|
782
|
|
Refused
|
27
|
41
|
10
|
9
|
88
|
|
Total
|
210
|
827
|
495
|
471
|
2003
|
|
Expected number Prime Minister(Pi )
|
Age(Aj ) 18-24
|
25-49
|
50-64
|
65+
|
|
Rishi Sunak
|
55.1473
|
217.1752
|
|
123.6875
|
|
Keir Starmer
|
63.5347
|
|
149.7604
|
142.4993
|
|
Not Sure
|
81.9870
|
322.8727
|
193.2551
|
183.8852
|
|
Refused
|
9.2262
|
36.3335
|
21.7474
|
20.6930
|
|
Joint probabilities Prime Minister(Pi )
|
Age (Aj ) 18-24
|
25-49
|
50-64
|
65+
|
Pr(Pi )
|
|
Rishi Sunak
|
0.0275
|
0.1084
|
|
0.0618
|
|
|
Keir Starmer
|
0.0317
|
|
0.0748
|
0.0711
|
|
|
Not Sure
|
0.0409
|
0.1612
|
0.0965
|
0.0918
|
0.3904
|
|
Refused
|
0.0046
|
0.0181
|
0.0109
|
0.0103
|
0.0439
|
|
Pr(Aj )
|
0.1048
|
|
|
0.2351
|
1
|