“software” method is based on the formula given in Chapter 11 . The second way of computing degrees
of freedom is the “conservative” method introduced in Chapter 11 .example: A statistics teacher, Mr. Srednih, gave a quiz to his 8:00 AM class and to his 9:00 AM
class. There were 50 points possible on the quiz. The data for the two classes were as follows.Before the quiz, some members of the 9:00 AM class had been bragging that later classes do better in
statistics. Considering these two classes as random samples from the populations of 8:00 AM and 9:00 AM
classes, do these data provide evidence at the .01 level of significance that students in 9:00 AM classes do
better than those in 8:00 AM classes?
solution:I . Let μ 1 = the true mean score for the 8:00 AM class.
Let μ 2 = the true mean score for the 9:00 AM class.
H 0 : μ 1 – μ 2 = 0.H (^) A : μ 1 – μ 2 < 0.
II . We will use a two-sample t -test at α = 0.01. We assume these samples are random samples
from independent populations. t -procedures are justified because both sample sizes are
larger than 30.
(Note: If the sample sizes were not large enough, we would need to know that the samples
were drawn from populations that are approximately normally distributed.)
III. , df = min{34 – 1, 31 – 1} = 30.
From Table B, 0.005 < P -value < 0.01. Using the tcdf function from the DISTR menu of the
TI-83/84 yields tcdf(-100,-2.53,30)=0.0084 . Using the 2SampTTest function in the
STAT TESTS menu of the TI-83/84 for the whole test yields t = –2.53 and a P -value of
0.007 based on df = 49.92 (the lower P -value being based on a larger number of degrees of
freedom).
IV . Because P < 0.01, we reject the null hypothesis. We have good evidence that the true mean
for 9:00 AM classes is higher than the true mean for 8:00 AM classes.
Inference for a Single Population Proportion
We are usually more interested in estimating a population proportion with a confidence interval than we
are in testing that a population proportion has a particular value. However, significance testing techniques