Question

1. A health insurance broker records the monthly extended health and dental insurance premiums for 18 non-smoking white-collar clients between the ages of 31 and 40 (measured in $):

109	88	129	97	151	141	48	109	57
86	117	56	127	113	124	72	132	58

a. Calculate the sample mean ( x̄) and standard deviation (s) to the nearest cent.

b. Construct a 98% confidence interval for the mean monthly insurance premium for all non-smoking white-collar clients between the ages of 31 and 40.

2. Calculate the margin of error and construct a confidence interval for the population proportion using the normal approximation to the  p̂  p̂ -distribution (if it is appropriate to do so).

a. p̂ =0.9, n=160,  α =0.2, E = ? ( four decimal places)

b. p̂ =0.6, n=140,  α =0.05 , E = ? (four decimal places)

Answer 1

mean	100.78
sample standard deviation	32.04
sample variance	1,026.30
confidence interval 98.% lower	81.40
confidence interval 98.% upper	120.16
margin of error	19.38
t(df = 17)	2.567

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a. Calculate the sample mean ( x̄) and standard deviation (s) to the nearest cent.

sample mean ( x̄) = 100.78

standard deviation (s) =32.04

b. Construct a 98% confidence interval for the mean monthly insurance premium for all non-smoking white-collar clients between the ages of 31 and 40.

81.40<u<120.16

2. Calculate the margin of error and construct a confidence interval for the population proportion using the normal approximation to the  p̂  p̂ -distribution (if it is appropriate to do so).

a. p̂ =0.9, n=160,  α =0.2, E = ? ( four decimal places)

80%	confidence level
0.9	proportion
160	n
1.282	z
0.0304	margin of error,E
0.8696	lower confidence limit
0.9304	upper confidence limit

b. p̂ =0.6, n=140,  α =0.05 , E = ? (four decimal places)

95%	confidence level
0.6	proportion
140	n
1.960	z
0.0812	margin of error,E
0.5188	lower confidence limit
0.6812	upper confidence limit