Question

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) Which of these are 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?
H0: µ < 6 vs. Ha: µ = 6
H0: µ = 6 vs. Ha: µ ? 6
H0: µ = 6 vs. Ha: µ < 6
H0: µ = 6 vs. Ha: µ > 6

(b) Suppose the mean litter size for sampled females was found to be 5.913 (thus, less than 6), and the standard deviation was 1.139. Find the standardized sample mean, under the assumption that the null hypothesis is true. (Round your answer to two decimal places.)

(c) Should we identify the standardized sample mean as z or as t?

(d) Based on your alternative hypothesis, what kind of probability would the P-value be?
left-tailed probability
two-tailed probability
right-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 size of the P-value.
not small at all somewhat small
quite small extremely small (close to zero)

(f) Do the data provide evidence that mean litter size for all captive female striped skunks is less than 6?
Yes
No
borderline

Answer 1

a) H₀: = 6 vs. H_a: < 6

b) The test stastistic

  

  

c) We identified the standardized sample mean as t.

d) left-tailed probability

e) P-value = P(T < -0.31)

               = 0.3804

The size of the P-value is not small at all.

f) No, the data don't provide evidence that mean litter size for all captive female striped skunks is less than 6.