Question

Height (inches)	Sleep (hours)	Gender
61	7	M
62	7	F
63	5	F
63	7	F
64	6	F
65	8	F
65	7	F
66	8	F
66	5	M
67	8	M
67	8	F
67	4	F
67	8	F
68	8	M
68	6	M
69	8	M
69	8	M
69	8	M
69	7	F
69	10	M
69	6	F
69	7	M
70	8	F
70	5	F
70	8	F
70	7	F
70	7	M
71	4	M
71	9	M
71	8	M
73	7	F
73	7	M
74	8	M
74	8	M
75	10	M

1. Give and interpret the 95% confidence interval for the hours of sleep a student gets.
2. Give and interpret the 99% confidence interval for the hours of sleep a student gets.
3. Compare the 95% and 99% confidence intervals for the hours of sleep a student gets. Explain the difference between these intervals and why this difference occurs

Answer 1

1. Give and interpret the 95% confidence interval for the hours of sleep a student gets.

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	1.4100
Sample Mean	7.2
Sample Size	35
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	0.2383
Degrees of Freedom	34
t Value	2.0322
Interval Half Width	0.4844
Confidence Interval
Interval Lower Limit	6.7156
Interval Upper Limit	7.6844

95% CI for mean hours of sleep a student gets is (6.7156,7.6844).

We are 95% confident that average hours of sleep of all students gets falls in the interval (6.7156,7.6844).

2. Give and interpret the 99% confidence interval for the hours of sleep a student gets.

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	1.4100
Sample Mean	7.2
Sample Size	35
Confidence Level	99%
Intermediate Calculations
Standard Error of the Mean	0.2383
Degrees of Freedom	34
t Value	2.7284
Interval Half Width	0.6503
Confidence Interval
Interval Lower Limit	6.5497
Interval Upper Limit	7.8503

99% CI for mean hours of sleep a student gets is (6.5497, 7.8503).

We are 99% confident that average hours of sleep of all students gets falls in the interval (6.5497, 7.8503).

3. Compare the 95% and 99% confidence intervals for the hours of sleep a student gets. Explain the difference between these intervals and why this difference occurs

99% confidence intervals for the hours of sleep is wider than the 95% confidence intervals for the hours of sleep. This is because the reliability factor ( t value) for 99% CI is larger than 95% CI.