Question

Wellpoint is a health insurer that provides online video doctor visits as a way to save patients money. Below are the amounts saved ($) by a sample of patients in 2014. Use it to answer/do thefollowing. 92 105 56 76 93 78 53 34 83 49 90 45

(a) Estimate the average savings.

(b) Develop a 90% con dence interval for the mean in (a).

(c) Develop a 95% con dence interval for the mean in (a)

.(d) Develop a 99% con dence interval for the mean in (a).

(e) Would it be okay for Wellpoint to claim they save patients about $100 on average?

(f) Would it be okay for Wellpoint to claim they save patients about $80 on average?

Answer 1

(a)

Average saving = = 854/12 = 71.17

(b)

Sample Standard deviation s = 22.8387

SE = s/

= 22.8387/ = 6.5930

= 0.10

ndf = n - 1 = 12 - 1 = 11

From Table, critical values of t = 1.7959

Confidence interval:

71.17 (1.7959 X 6.5930)

= 71.17 11.8403

= ( 59.33 ,83.01)

So,

Confidence Interval:

59.33 < < 83.01

(c)

Sample Standard deviation s = 22.8387

SE = s/

= 22.8387/ = 6.5930

= 0.05

ndf = n - 1 = 12 - 1 = 11

From Table, critical values of t = 2.2010

Confidence interval:

71.17 (2.2010 X 6.5930)

= 71.17 14.5112

= ( 56.66 ,85.68)

So,

Confidence Interval:

56.66 < < 85.68

(d)

Sample Standard deviation s = 22.8387

SE = s/

= 22.8387/ = 6.5930

= 0.01

ndf = n - 1 = 12 - 1 = 11

From Table, critical values of t = 3.1058

Confidence interval:

71.17 (3.1058 X 6.5930)

= 71.17 20.4765

= ( 50.69 ,91.65)

So,

Confidence Interval:

50.69 < < 91.65

(d)

(i)

Since100 is not included in the confidence Interval, it would not be okay for Wellpoint to claim that they save patients about $100 on average.

(ii)

Since 80 is included in the confidence Interval, it would be okay for Wellpoint to claim that they save patients about $80 on average.