Estrus synchronization products are used to bring cows into heat at a predictable time so that they can be reliably impregnated by artificial insemination. In a study of two estrus synchronization products, 42 mature cows (ages 4-8 years) were randomly allocated to receive either product A or product B, and then all cows were bred by artificial insemination. The table shows how many of the inseminations resulted in pregnancy. Consider a chi-square test to compare the effectiveness of the two products in producing pregnancy.

Here is computer output for a chi-square test using a non-directional alternative.
X-squared = 4.71, df = 1, p-value = 0.03
(a) State the null and alternative hypotheses in context.
(b) Compute the expected frequencies.
(c) If α = 0.05. what is your conclusion regarding H0?
(d) Suppose that prior to conducting the study, the researchers were expecting product A to be superior to product B. Using α = 0.05 and a directional alternative, what is your conclusion'.'

Transcribed Image Text:

Treatment Product A 21 Product B 21 15 Total number of cows Number of cows pregnant 8