An article on spatial organization of the honey badger in the southern Kalahari, published in the Journal of Zoology in 2005, reported home range sizes in square kilometers for four females and four males (not their mates) in the dry season and then for the same badgers in the wet season.
a. If a comparison is to be made between home range sizes for females versus males, would a paired or two-sample procedure be used?
b. If a comparison is to be made between home range sizes for females versus males, should we do inference about the mean of differences or difference between means?
c. If a comparison is to be made between home range sizes in the dry versus the wet season, would a paired or a twosample procedure be used?
d. If a comparison is to be made between home range sizes in the dry versus the wet season, should we do inference about the mean of differences or the difference between means?
e. Judging from the numbers in the table, which difference is more dramatic-the one between males and females or the one between dry and wet season?
f. Use software to test if, for all female honey badgers, it is plausible that the mean of differences between home range sizes, wet minus dry season, equals zero; first report the t statistic.
g. Report the P-value for the test in part (f).
h. State your conclusion.
i. For female badgers, report a 95% confidence interval for the mean of all differences in home range sizes, wet minus dry season.
j. Use software to test if, for all males, it is plausible that the mean of differences between home range sizes, wet minus dry season, equals zero; first report the t statistic.
k. Report the P-value for the test in part (j).
l. State your conclusion.
m. For male badgers, report a 95% confidence interval for the mean of all differences in home range sizes, wet minus dry season.
n. Use software to test if the mean home range size in the dry season for all female honey badgers could equal that for all males: first report the t statistic.
o. Report the P-value for the test in part (n).
p. State your conclusion.
q. For the dry season, report a 95% confidence interval for the difference in mean home range sizes, females minus males.
r. What would the P-value in part (o) be if we suspected in advance that home range size in the dry season is greater for males than for females?
s. Use software to test if the mean home range size in the wet season for all female honey badgers could equal that for all males; first report the t statistic.
t. Report the P-value for the test in part (s).
u. State your conclusion.
v. For the wet season, report a 95% confidence interval for the difference in mean home range sizes, females minus males.
w. What would the P-value in part (t) be if we suspected in advance that home range size in the wet season is greater for males than for females?
x. Which of these apparently has a significant effect on honey badgers' home range size: type of season (wet or dry), gender, both, or neither?
y. Consider the four hypothesis tests and the four confidence intervals produced in this exercise. What can we say about the confidence intervals when the data led us to reject the null hypothesis?
z. The researchers actually had data from about twice as many badgers, with results similar to those shown in the previous table. With a bigger sample size, would the P-values for your tests be larger or smaller?