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Hi Sandhya! It's me again, do...

Hi Sandhya!

It's me again, do you think you could help me with this homework? Deadline is 7 hours from now. Really need help!

QUESTION 1

Before launching a new online service, a bank is interested in estimating the percentage of customers that are potentially interested in the new service. In particular the bank wants to derive the confidence interval, at 90 % of confidence, for such a proportion with a maximum error of ± 0.05 (± 5 %) with respect to the true population proportion. How many customers should be included in a sample?

QUESTION 2

It is given a population X normally distributed with unknown mean μ and known standard deviation = 0.012

i) What is the optimal sample size if we want to estimate the population mean with a maximum error of 0.1 at a confidence level of 95 % ?

ii) Assume now that we have observed a sample of dimension n = 6 from such a population and that we obtain the following data:

25 24 25 24 25 25

Determine the confidence interval of the mean at a confidence level of 99%.

QUESTION 3

Three classes of students take an exam in statistics on the same day. In the first class there are 15 students, 16 in the second and 14 in the third. The Professor distributes three different exam texts in the three classes. The grades obtained by the students in the midterm exam are reported here below (the maximum grade is 50).

Student ID. Class 1. Class 2. Class 3.

1 34 42 50

2 36 45 37

3 32 36 48

4 37 28 44

5 36 40 25

6 24 37 33

7 31 39 39

8 28 41 43

9 22 44 41

10 22 42 37

11 34 45 43

12 23 29 28

13 33 35 34

14 30 21 45

15 34 28 --

16 -- 44 --

Test the hypothesis that for the three exams the mean population grade is 37.

QUESTION 4

The owner of a large shopping center is interested in anticipating the percentage of potential electors that are incline to vote for him before deciding to formally present his candidacy to the next elections as the mayor of the town. He commission a survey to have advise in this direction. In the survey, apart from the percentage of votes he is likely to obtain, the candidate wants also to gain some information about the mean expenses of the village population. He knows, from some credit card information he received anonymously for a local bank, that the maximum amount of monthly expenses in the village is 3,000 $.

i) How large has to be the sample size if we wish to estimate the proportion of his votes with a maximum error of ± 2% and the mean expenses with a maximum error of ± 500 $, both at a level of confidence of 95 % ?

ii) Now supposte that the statistical consultant in charge of the consultancy decides to draw a sample of dimension n = 200 citizens of the town and that in the sample the proportion of votes for the candidate is p = 0.52. Build up a confidence interval on this proportion at 95 % confidence level.

iii) Suppose also that in the same sample the sample mean is m = 2,800 $ and the estimated (unbiased) sample variance is 350 $. Build up a confidence interval for the population mean at 95 % confidence level.

It's me again, do you think you could help me with this homework? Deadline is 7 hours from now. Really need help!

QUESTION 1

Before launching a new online service, a bank is interested in estimating the percentage of customers that are potentially interested in the new service. In particular the bank wants to derive the confidence interval, at 90 % of confidence, for such a proportion with a maximum error of ± 0.05 (± 5 %) with respect to the true population proportion. How many customers should be included in a sample?

QUESTION 2

It is given a population X normally distributed with unknown mean μ and known standard deviation = 0.012

i) What is the optimal sample size if we want to estimate the population mean with a maximum error of 0.1 at a confidence level of 95 % ?

ii) Assume now that we have observed a sample of dimension n = 6 from such a population and that we obtain the following data:

25 24 25 24 25 25

Determine the confidence interval of the mean at a confidence level of 99%.

QUESTION 3

Three classes of students take an exam in statistics on the same day. In the first class there are 15 students, 16 in the second and 14 in the third. The Professor distributes three different exam texts in the three classes. The grades obtained by the students in the midterm exam are reported here below (the maximum grade is 50).

Student ID. Class 1. Class 2. Class 3.

1 34 42 50

2 36 45 37

3 32 36 48

4 37 28 44

5 36 40 25

6 24 37 33

7 31 39 39

8 28 41 43

9 22 44 41

10 22 42 37

11 34 45 43

12 23 29 28

13 33 35 34

14 30 21 45

15 34 28 --

16 -- 44 --

Test the hypothesis that for the three exams the mean population grade is 37.

QUESTION 4

The owner of a large shopping center is interested in anticipating the percentage of potential electors that are incline to vote for him before deciding to formally present his candidacy to the next elections as the mayor of the town. He commission a survey to have advise in this direction. In the survey, apart from the percentage of votes he is likely to obtain, the candidate wants also to gain some information about the mean expenses of the village population. He knows, from some credit card information he received anonymously for a local bank, that the maximum amount of monthly expenses in the village is 3,000 $.

i) How large has to be the sample size if we wish to estimate the proportion of his votes with a maximum error of ± 2% and the mean expenses with a maximum error of ± 500 $, both at a level of confidence of 95 % ?

ii) Now supposte that the statistical consultant in charge of the consultancy decides to draw a sample of dimension n = 200 citizens of the town and that in the sample the proportion of votes for the candidate is p = 0.52. Build up a confidence interval on this proportion at 95 % confidence level.

iii) Suppose also that in the same sample the sample mean is m = 2,800 $ and the estimated (unbiased) sample variance is 350 $. Build up a confidence interval for the population mean at 95 % confidence level.

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