Consider the sample of students at the University of Reading in Table 3. Table 3: Hours spent studying per week Student ID. Hours spent studying ID1. 1 ID2. 2 ID3. 3 ID4. 5 ID5. 4 ID6. 5 ID7. 7 ID8. 7 ID9. 12 ID10 5 ID11. 7 ID12 7 ID13 15 ID14. 0 ID15. 3 ID16. 4 ID17. 4 ID18 . 0 ID19. 5 ID20. 7 ID21. 7 ID22 . 13 ID23. 7 ID24. 9 a) Consider the possibility of using this sample to make some inference about the average number of hours that students at the University of Reading spend on studying. What estimator would you use? How is your estimator distributed? State the assumptions you used to answer the question. [Answer all sub-questions] (b) Do students at Reading study as much as recommended by national guidelines, i.e. 6 hours per week? Test the hypothesis that students at Reading University study on average as much as recommended by national guidelines using a 99% confidence interval. For this answer assume that the population is normally distributed, and that the variance is known and equal to 10. Show the workings and interpret your findings (c) Instead of accepting any prior view on the variance, use the sample variance instead. Explain in words how the procedure you are going to use differs from the one used in b) and calculate the 99% confidence interval. Show the workings and interpret your findings. (d) Obtain the same answer as above by writing down the null and alternative hypothesis and provide a statistical test to support the claim with the same level of confidence. Show the workings and interpret your findings. (e) If the same average and variance used above in c) were obtained from a sample of 5 students, how would the confidence interval change? How would the standardised sample mean and its distribution change? [Answer all subquestions
5. Inference.
Consider the sample of students at the University of Reading in Table 3.
Table 3: Hours spent studying per week
Student ID. Hours spent studying
ID1. 1
ID2. 2
ID3. 3
ID4. 5
ID5. 4
ID6. 5
ID7. 7
ID8. 7
ID9. 12
ID10 5
ID11. 7
ID12 7
ID13 15
ID14. 0
ID15. 3
ID16. 4
ID17. 4
ID18 . 0
ID19. 5
ID20. 7
ID21. 7
ID22 . 13
ID23. 7
ID24. 9
a) Consider the possibility of using this sample to make some
inference about the average number of hours that students at
the University of Reading spend on studying. What estimator
would you use? How is your estimator distributed? State the
assumptions you used to answer the question. [Answer all
sub-questions]
(b) Do students at Reading study as much as recommended by
national guidelines, i.e. 6 hours per week? Test the
hypothesis that students at Reading University study on
average as much as recommended by national guidelines
using a 99% confidence interval. For this answer assume
that the population is
variance is known and equal to 10. Show the workings and
interpret your findings
(c) Instead of accepting any prior view on the variance, use the
sample variance instead. Explain in words how the
procedure you are going to use differs from the one used in
b) and calculate the 99% confidence interval. Show the
workings and interpret your findings.
(d) Obtain the same answer as above by writing down the null and
alternative hypothesis and provide a statistical test to support
the claim with the same level of confidence. Show the
workings and interpret your findings.
(e) If the same average and variance used above in c) were
obtained from a sample of 5 students, how would the
confidence interval change? How would the standardised
sample
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