- 17.1 Matched pairs
- 17.2 Two independent samples
- 17.3 Single sample
- 17.4 Two independent samples
- 17.8
- a) If the loggers knew that the effects of logging would be
assessed, they may log in such a way as to try to minimize the effect.
If they did not normally log in this manner, it would not be possible
to generalize to logging practices at other times and locations.
- b) H0: μL-μUL=0,
there is no difference in the mean number of species between logged and
unlogged plots 8 years after logging.
Ha: μL - μUL< 0, the
mean number of species in logged plots is less than the mean number of
species in unlogged plots 8 years after logging.
The t-statistic is 2.1141. Using the conservative value of
8 degrees of freedom, the p-value is between .05 and .025 for the
one-sided alternative. The test is significant at the .05 level, but
not the .025 level.
- 17.10 A 90% confidence interval (using a conservative 8
degrees of freedom) for the difference in the mean number of species
between logged and unlogged plots is
3.8 ± 1.86*1.81 or (.433, 7.27).
- 17.12 The two-sample t confidence interval for the
difference in mean yields may not be accurate because the sample size
is smaller than the recommended minimum of 5 in each group.
- 17.24
- a)H0: μF=μM, the
mean score for females is the same as the mean score for males.
Ha: μF<μM, the mean
score for females is lower than the mean score for males.
The test statistic t=6.13. The p-value is less than .0005. There
is strong statistical evidence that the mean score on the interview
questions is lower for women than men.
- b) A sample of drivers selected by random digit dialing may
not be representative of the population of drivers.
- 17.26 H0: μ9=μ11, the
students in grades 9 and 11 have the same mean score on the CDI.
Ha: μ9<μ11, the students
in grade 9 have a mean score lower than those in grade 11 on the CDI.
The test statistic t=1.9. Taking 69 as the conservative degrees
of freedom, the p-value for the one-sided test is between .05 and .025.
Therefore, there is statistically significant evidence that 11th
graders score higher on the CDI than 9th graders.
- 17.27 H0: μM=μF, male
and female students have the same mean score on the CDI.
Ha: μM≠μF, male and
female students have different mean scores on the CDI.
The test statistic t=.25. Taking 103 as the conservative degrees
of freedom, the p-value for the one-sided test is greater than .25.
Therefore, there is no significant evidence that male and female
students have different mean scores on the CDI
- 17.28 H0: μT=μC,
The mean improvement in the treatment group is the same as the mean
change in the control group.
Ha: μT>μC, the mean
improvement for the treatment group is greater than the mean improvement
for the control group.
The test statistic t=1.91. The approximate degrees of freedom is
13.919. The p-value is 0.038, so the improvement of those in the
receiving the treatment was significantly greater than the improvement
of those receiving the neutral message. This is true at both the 5%
and 10% level.
- 17.30 A 90% confidence interval for the mean difference in
gains between treatment and control groups is (0.249, 6.051).
- 17.38
- a) The mean score for boys is 110.96 and the mean score for
girls is 105.84.
- b)
For Boys:
| 7 | 79 |
| 8 | |
| 9 | 0377 |
| 10 | 0234556667779 |
| 11 | 00001123334556899 |
| 12 | 0334467788 |
| 13 | 6 |
For Girls
| 7 | 24 |
| 8 | 69 |
| 9 | 1368 |
| 10 | 023334578 |
| 11 | 1122244489 |
| 12 | 08 |
| 13 | 02 |
- c)H0: μB=μG, the mean
score of boys on the IQ test is the same as the mean score of girls.
Ha: μB>μG, the mean
score of boys on the IQ test is the greater than the mean score of
girls.
The test statistic t=1.64, with an approximate degrees of freedom
of 56.9. The p-value=0.052.
- d) It would be important to know whether the students who
took the test are in fact representative of all 7th grade students in
the district.
- 17.40 The critical value for a 90% confidence interval given
a t-distribution with 56.9 degrees of freedom is 1.67. A 90% confidence
interval for the difference between the mean IQ scores of all boys and
girls in the district is (-0.088, 10.325).