Question

The data file below contains a sample of customer satisfaction ratings for XYZ Box video game system. If we let µ denote the mean of all possible customer satisfaction ratings for the XYZ Box video game system, and assume that the standard deviation of all possible customer satisfaction ratings is 2.64:

Ratings
39
45
38
42
42
41
38
42
46
44
40
39
40
42
45
44
42
46
40
47
44
43
45
45
40
46
41
43
39
43
46
45
45
46
43
47
43
41
40
43
44
41
38
43
36
44
44
45
44
46
48
44
41
45
44
44
44
46
39
41
44
42
47
43
45

(a) Calculate 95% and 99% confidence intervals for µ. (Round your answers to 3 decimal places.)

95% confidence interval for µ is	[, ].
99% confidence interval for µ is	[, ].

(b) Using the 95% confidence interval, can we be 95% confident that µ is at least 42 (recall that a very satisfied customer gives a rating of at least 42)?

(Click to select)NoYes , because if we are 95% confident that the interval contains μ, and the entire interval is (Click to select)belowabove 42, then we are 95% confident that μ is greater than 42.

(c) Using the 99% confidence interval, can we be 99% confident that µ is at least 42?

(Click to select)NoYes , because if we are 99% confident that the interval contains μ, and the entire interval is (Click to select)abovebelow 42, then we are 99% confident that μ is greater than 42.

(d) Based on your answers to parts b and c, how convinced are you that the mean satisfaction rating is at least 42?

(Click to select)Very confidentNot confident  based on the 99% confidence interval being (Click to select)belowabove 42.

Answer 1

Sample size, n = 65

σ = 2.64

Sample mean calculates, x̅ = 42.9538

a) 95% confidence interval:

Two tailed critical value, z_crit = NORM.S.INV(0.05/2) = 1.96

Lower Bound = x̅ - z_crit*σ/√n = 42.312   
Upper Bound = x̅ + z_crit*σ/√n = 43.596

99% confidence interval:

Two tailed critical value, z_crit = NORM.S.INV(0.01/2) = 2.576

Lower Bound = x̅ - z_crit*σ/√n = 42.110
Upper Bound = x̅ + z_crit*σ/√n = 43.797

--------------------

(b) Yes , because if we are 95% confident that the interval contains μ, and the entire interval is above 42, then we are 95% confident that μ is greater than 42.

(c) Yes , because if we are 99% confident that the interval contains μ, and the entire interval is above 42, then we are 99% confident that μ is greater than 42.

(d) Very confident based on the 99% confidence interval being above 42.