A Sample of Students from an Introductory Business Course WereA Based on the Sample Results, Find the 95% Confidence

Question

Examlex · Accepted Answer

The Answer is a. Based on the sample results, find the

95 \%

confidence interval.
The sample has a mean of

10.92

hours and a standard deviation of

5.60

hours.

\bar { y } \pm t _ { n - 1 } ^ { * } imes S E ( \bar { y } ) = 10.92 \pm 2.069 \frac { 5.60 } { \sqrt { 24 } } = 10.92 \pm 2.365

The

95 \%

confidence interval for true mean age is

8.5

to

13.3

hours.
b. Interpret the results.
We are

95 \%

confident that the average age of clients with recently paid policies is between

76.87

and

80.33

years.
c. Do you expect a

90 \%

confidence interval to be wider or narrower and why?
A

90 \%

confidence interval will be narrower because the margin of error will be smaller for a lower confidence level.
d. A previous study of a large cross-section of students in this course showed that students studies 12 hours per week. Are the results of this current study statistically different than the assumption of 12 hours per week studying? Define the hypotheses and compare the

t

-value to the critical

t

value, evaluating at

\alpha = 0.05

.
Hypotheses:

\mathrm { H } _ { 0 } : \mu = 12 \mathrm { hrs } ; \mathrm { H } _ { \mathrm { A } } : \mu eq 12 \mathrm { hrs }

t-test:

t = \frac { 10.92 - 12 } { 5.6 / \sqrt { 24 } } = - 0.945

; the critical

\mathrm { t }

value for

\mathrm { df } = 23

at

0.05 = \pm 2.0686

The calculated value is less than the critical value so the result is not statistically significant at

\alpha = 0.05

. There is no evidence that the level of studying has changed.

A Sample of Students from an Introductory Business Course Were

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