Calculus and Above

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Hi Sandhya, it's me again...

Hi Sandhya, it's me again. Can you complete these questions with a deadline 8 hours from now? Would highly appreciate your help.

Question 1

In a statistical test on the mean the p-value is equal to 0.049. What is your decision on the null hypothesis H0 if you want to take this decision with a level of confidence of 95 % ?

Question 2

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 at a level of confidence of 90 % using the t-student distribution for your test statistics.

Question 3

An industry produces batteries for cell phones of two typologies: Nickel-Cadmium and Nickel-Metal Hydride. The average recharging time of the Nickel-Cadmium batteries is of 71.1 hours. We draw randomly 10 Nickel-Metal Hydride batteries and we evaluate their recharging time (in hours), reported here below:

78.3 95.4 69.4 87.3 62.5 85.0 85.3 72.1 81.3 72.5

a) On the basis of this sample information, build up a confidence interval for the average recharging time of the Nickel-Metal Hydride batteries at the level of confidence of 98 %.

b) Test the hypothesis that the Nickel-Metal Hydride have a significantly higher recharging time than the Nickel-Cadmium with a level of significance of 98 %. Use the appropriate alternative hypothesis

c) Comment the results obtained in point a) and in point b).

Question 4

The mean expenditure of the customers of a big grocery store is 40 $ and we can assume that the population standard deviation is 9 $. After a campaign the manager of the store wants to test if it was effective in raising the level of average consumption. He observes a sample of 11 customers and finds a sample mean expenditure of 44 $.

a) Test the hypothesis that the campaign was effective at a level of confidence of 10 %;

b) Let us now consider the case in which we cannot assume the population variance as known and that in the sample we found a standard deviation of 9.2 $. Repeat the test under this new assumption at the same level of significance.

c) Comment the results obtained in point a) and in point b)

Question 5

A sample of 30 electors are surveyed to gain information about the intention to vote at the next presidential elections. These are the results obtained:

Individual. Answer.

1 candidate A

2 candidate B

3 candidate B

4 candidate A

5 candidate A

6 candidate B

7 candidate A

8 candidate B

9 candidate A

10 candidate A

11 candidate B

12 candidate A

13 candidate B

14 candidate A

15 candidate B

16 candidate A

17 candidate A

18 candidate B

19 candidate A

20 candidate B

21 candidate A

22 candidate A

23 candidate B

24 candidate A

25 candidate B

26 candidate A

27 candidate A

28 candidate B

29 candidate A

30 candidate A

Test the hypothesis that the candidate A will obtain more than 50% of votes at a level of confidence of 96 %.

Question 1

In a statistical test on the mean the p-value is equal to 0.049. What is your decision on the null hypothesis H0 if you want to take this decision with a level of confidence of 95 % ?

Question 2

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 at a level of confidence of 90 % using the t-student distribution for your test statistics.

Question 3

An industry produces batteries for cell phones of two typologies: Nickel-Cadmium and Nickel-Metal Hydride. The average recharging time of the Nickel-Cadmium batteries is of 71.1 hours. We draw randomly 10 Nickel-Metal Hydride batteries and we evaluate their recharging time (in hours), reported here below:

78.3 95.4 69.4 87.3 62.5 85.0 85.3 72.1 81.3 72.5

a) On the basis of this sample information, build up a confidence interval for the average recharging time of the Nickel-Metal Hydride batteries at the level of confidence of 98 %.

b) Test the hypothesis that the Nickel-Metal Hydride have a significantly higher recharging time than the Nickel-Cadmium with a level of significance of 98 %. Use the appropriate alternative hypothesis

c) Comment the results obtained in point a) and in point b).

Question 4

The mean expenditure of the customers of a big grocery store is 40 $ and we can assume that the population standard deviation is 9 $. After a campaign the manager of the store wants to test if it was effective in raising the level of average consumption. He observes a sample of 11 customers and finds a sample mean expenditure of 44 $.

a) Test the hypothesis that the campaign was effective at a level of confidence of 10 %;

b) Let us now consider the case in which we cannot assume the population variance as known and that in the sample we found a standard deviation of 9.2 $. Repeat the test under this new assumption at the same level of significance.

c) Comment the results obtained in point a) and in point b)

Question 5

A sample of 30 electors are surveyed to gain information about the intention to vote at the next presidential elections. These are the results obtained:

Individual. Answer.

1 candidate A

2 candidate B

3 candidate B

4 candidate A

5 candidate A

6 candidate B

7 candidate A

8 candidate B

9 candidate A

10 candidate A

11 candidate B

12 candidate A

13 candidate B

14 candidate A

15 candidate B

16 candidate A

17 candidate A

18 candidate B

19 candidate A

20 candidate B

21 candidate A

22 candidate A

23 candidate B

24 candidate A

25 candidate B

26 candidate A

27 candidate A

28 candidate B

29 candidate A

30 candidate A

Test the hypothesis that the candidate A will obtain more than 50% of votes at a level of confidence of 96 %.

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