In "Reproduction, Growth and Development in Captive Beluga," published in the journal Zoo Biology in 2005, researchers observed captive male beluga whales in various aquariums. Number of calves sired was recorded for all 10 males included in the study.
a. Formulate the appropriate null and alternative hypotheses (using mathematical symbols) if we want to test whether the mean number of calves sired by all captive male belugas exceeds 1.0.
b. The mean number of calves sired by sampled males was found to be 1.4 (thus, greater than 1) and the standard deviation was 1.35. Find the standardized sample mean.
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 10), 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 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 number of calves sired by all male beluga whales in captivity exceeds 1.0.