602 / 762
602
Chapter 13: Confidence Intervals – Small Samples
If we wanted to use the formula, we would have to carry out the
computations and substitute into the formula to compute the confidence
interval. Also, since raw data are given, we will have to compute the sample
means and sample variances. Thus, from the information given, we have
= 10,
= 10,
̅
= 13.6,
̅
= 13.7,
= 3.2042,
= 2.8694,
(
)
(
)
= 9.2052
,
=
3.0414,
= 0.02,
/2 = 0.01,
df
= 10 + 10 –
2 = 18,
= 2.5524, and
√
=
√
= 0.4472.
Thus, the 98 percent confidence interval estimate for the difference in the
mean times to complete the project by the male and female students is
(13.6 – 13.7)
2.5524
3.0414
0.4472 = -0.1
3.4716. That is, we are 98
percent confident that the difference between the means for the two
populations (average time for the male students - average for the female
students) is (-3.5716, 3.3716). That is, we are 98% confident that the
difference between the two population means will lie between -3.5716 and
3.3716. Thus, we will have the same conclusion that the instructor may
claim that the female and male students, on average, will spend the same
amount of time on the project.
Section Review
13-5 Small Sample Confidence Interval for the Difference
Between Two Population Means Using Dependent
Samples
e-Self Review Click here for the Small Sample Confidence Interval for the Difference Between Two Independent Means Workbook