Question

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?

$h_{0}$: the distribution of births is uniform across the days of the week. $h_{a}$: the distribution of births is not uniform across the days of the week.

$h_{0}$: the distribution of births is not uniform across the days of the week. $h_{a}$: the distribution of births is uniform across the days of the week.

$h_{0}$: the sample of 350 births is distributed so that 50 births occur each day of the week. $h_{a}$: the sample of 350 births is not distributed so that 50 births occur each day of the week.

$h_{0}$: the sample of 350 births is not distributed so that 50 births occur each day of the week. $h_{a}$: the sample of 350 births is distributed so that 50 births occur each day of the week.

Explanation:

In hypothesis testing for distribution uniformity, the null hypothesis \(H_0\) represents the claim of uniformity (the default, no - difference situation). The alternative hypothesis \(H_a\) is the claim of non - uniformity. The sample size and specific counts (like 50 births per day) are not part of the hypotheses about the distribution (the hypotheses are about the population distribution, not the sample distribution in terms of exact counts).

Answer:

\(H_0\): The distribution of births is uniform across the days of the week. \(H_a\): The distribution of births is not uniform across the days of the week.