In "Husbandry, Overwinter Care, and Reproduction of Captive Striped Skunks," published in the journal Zoo Biology in 2005, researchers recorded litter size of 16 captured female striped skunks.
a. Formulate the appropriate null and alternative hypotheses (using mathematical symbols) if we want to test whether the mean litter size for all captive female striped skunks is less than 6.
b. The mean litter size for sampled females was found to be 5.813 (thus, less than 6), and the standard deviation was 1.109. Find the standardized sample mean, under the assumption that the null hypothesis is true.
c. Explain why the standardized sample mean should be identified as t and not z.
d. Based on your alternative hypothesis, would the P-value be a left-tailed, righttailed, or two-tailed probability?
e. For most t distributions (including that for samples of size 16), values between 0 and +1 are quite common; values close to +2 may be considered borderline, values close to +3 are unusually large, and values considerably greater than 3 in absolute value are extremely large. Characterize the P-value as being not small at all, somewhat small, quite small, or extremely small (close to zero).
f. Tell whether or not the data provide evidence that mean litter size for all captive female striped skunks is less than 6.
g. Researchers considered separately three females who gave birth in 2002, each with a litter size of 7. Explain why the sample standard deviation in this case is zero.
h. Why would the mechanics of the t test prevent us from finding a standardized sample mean, based on the data in part (g)?