Question

Student # Gender Height Shoe Age Hand

1 F 68 8.5 20 R

2 F 60 5.5 27 R

3 F 64 7 31 R

4 F 67 7.5 19 R

5 F 65 8 20 R

6 F 66 9 29 R

7 F 62 9.5 30 L

8 F 63 8.5 18 R

9 F 60 5 19 L

10 F 63 7.5 42 R

11 F 61 7 20 R

12 F 64 7.5 17 R

13 F 65 8 19 R

14 F 68 8 19 R

15 F 63 7.5 18 R

16 F 62 7.5 19 R

17 F 64 7 23 R

18 F 72 11 28 R

19 F 62 8 20 R

20 F 59 6.5 29 R

21 F 64 8.5 19 R

22 F 68 9.5 23 R

23 F 65 9.5 34 R

24 F 63 8 27 R

25 F 65 8 23 R

26 F 62 7.5 30 R

27 F 67 7.5 31 L

28 F 66 9 37 R

29 F 61 6 24 R

30 F 61 6.5 46 R

31 F 68 8 20 R

32 F 63 7.5 42 R

33 F 63 5.5 33 R

34 F 63 9 35 R

35 F 65 8 44 R

36 F 69 9 28 R

37 F 68 9 20 R

38 F 63 7 49 R

39 F 62 6.5 19 R

40 F 66 7.5 19 R

41 F 69 7.5 55 R

42 F 69 11 40 R

43 F 63 6.5 19 R

44 F 61 7.5 20 R

45 F 68 9 19 R

Round sample mean, standard deviation, z-scores to 3 decimal places. When finding sample size, state your answer as a whole number.

1. The number line below shows a hypothetical confidence interval for a population mean.

a. What is the width of the confidence interval?

b. What is the sample mean?

c. What is the margin of error?

Use the heights from the SCC data to answer the following questions. Men are to use the male data, and women are to use the female data (only answer the questions for ONE set of data, not both).

2. State the following for the SCC sample female/male heights.

a. Sample size (n)

b. Sample mean (???)

c. Sample standard deviation (s)

3. Use the sample to make a point estimate of the mean height of the entire female/male SCC student body.

4. (a) Construct a 93% confidence interval for the mean height of the entire female/male SCC student body. (Round to 2 decimal places)

(b) What is the width of this interval? (Round to 2 decimal places)

5. (a) Construct a 99% confidence interval for the mean height of the entire female/male SCC student body. (Round to 2 decimal places)

(b) What is the width of this interval? (Round to 2 decimal places)

6. Review your 93% and 99% confidence intervals above. Which is wider and why?

7. Suppose that next year we again will collect data and will want to estimate the mean height of the entire female/male SCC student body. The minimum sample size we need to take depends on what confidence level and margin of error we specify.

a. Determine the minimum sample size needed to be 94% confident that the sample mean we get is within ¼ inch of the true mean.

b. Determine the minimum sample size needed to be 94% confident that the sample mean is within ½ inch of the true mean.

c. Determine the minimum sample size needed to be 90% confident that the sample mean is within ½ inch of the true mean.

8. Answer the following using your answers from question 7 above.

a. Which sample size requirement in #7a and #7b is larger and why?

b. Which sample size requirement in #7b and #7c is larger and why?

Answer 1

as per company policies, I am answering question one only.

2. State the following for the SCC sample female heights.

A. Sample size (n)

N= 45.00 COUNT

B. Sample mean (???)

Mean= 64.44 AVERAGE

C. Sample standard deviation (s)

Sd= sqrt(var) 2.95 STDEV

3)

Point estimate of the mean height of the entire female SCC student body.

Sample mean = Xbar = 64.44

4)

a)

93% confidence interval for the mean height of the entire female SCC student body

z(a/2)
z(0.07/2)
1.812
CI = mean +- z(a/2)*(sd/sqrt(n))
lower = 64.4444 - 1.812*(2.95077459441935/sqrt(45))= 63.65
upper = 64.4444 + 1.812*(2.95077459441935/sqrt(45))= 65.24

b)

width of this interval = ME = z(a/2)*(sd/sqrt(n))

=1.812*(2.95077459441935/sqrt(45)) = 0.80