Conducting a Chi-Square Test for Goodness of Fit — Quiz
Question 8 • Statistics
A researcher would like to investigate if the distribution of the number of babies born is uniform across the days of the week. To investigate, the researcher selects a random sample of 350 babies and records on which day of the week they were born. The researcher would like to know if there is convincing evidence that the distribution of births is uniform across the days of the week. What are the appropriate hypotheses?
Answer
A
cap h sub 0 : The distribution of births is not uniform across the days of the week. cap h sub A : The distribution of births is uniform across the days of the week.
B
cap h sub 0 : The sample of 350 births is distributed so that 50 births occur each day of the week. cap h sub A : The sample of 350 births is not distributed so that 50 births occur each day of the week.
C
cap h sub 0 : The sample of 350 births is not distributed so that 50 births occur each day of the week. cap h sub A : The sample of 350 births is distributed so that 50 births occur each day of the week.
D
cap h sub 0 : The distribution of births is uniform across the days of the week. cap h sub A : The distribution of births is not uniform across the days of the week.
Explanation
The null hypothesis states the proposed distribution: births are equally likely on each of the seven days of the week. The alternative is that the distribution is not uniform, meaning at least one day has a different birth probability. These hypotheses concern the population distribution, not the sample’s exact counts, so the correct choice is D.
AI-written and checked against the verified answer.