Question

# 3. (a) Use the sample to make a point estimate of the mean height of the...

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

(b) Construct a 93% confidence interval for the mean height of the entire female/male SCC student body.

(c) What is the width of this interval?

(d) Write a sentence interpreting your confidence interval.

male Student # Gender Height Shoe Age Hand

1 M 67 10 19 R

2 M 74 12 17 R

3 M 72 11.5 19 R

4 M 69 10 35 R

5 M 66 9 18 R

6 M 71 10.5 17 R

7 M 72 10.5 17 R

8 M 66 10 20 R

9 M 67 10 18 R

10 M 71 10.5 24 R

11 M 66 10 21 R

12 M 71 10.5 18 R

13 M 69 10 22 R

14 M 66 9.5 18 L

15 M 76 14 18 R

16 M 69 11 22 R

17 M 68 9 19 R

18 M 70 12 30 R

19 M 67 10 24 R

20 M 70 11 21 R

21 M 70 10 52 R

22 M 63 9 27 R

23 M 69 11 22 R

24 M 72 10 22 R

25 M 76 11.5 20 L

26 M 75 11 17 R

27 M 72 11 50 L

28 M 69 11 20 R

29 M 70 12 20 R

30 M 69 11.5 23 R

31 M 70 11 18 R

32 M 67 10 21 R

33 M 68 11 44 R

34 M 76 13 48 R

35 M 62 8 23 L

36 M 69 9 19 R

37 M 72 10 60 R

38 M 73 11.5 41 R

39 M 70 9.5 39 R

40 M 78 15 24 R

41 M 65 8.5 23 R

42 M 68 9.5 20 R

5 a)Point estimate of the mean height =  Sample mean of the average height of the entire student body is

b) Sample standard deviation of the average height of the student body

Since the population standard deviation is unknown, hence we will use the t-statistics to find the 93% confidence interval for the population means.

The confidence interval for mean is given by

Degree of freedom = n- 1 = 42-1 = 41

93% confidence interval for the population mean is

c) Width of 93% confidence interval = 70.774 - 68.746 = 2.028

d) Interpretation: There is a 93% chance that the true average height will lie in the interval calculated above.