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. are the conditions for inference met?
no, the random condition is not met.
no, the 10% condition is not met.
no, the large counts condition is not met.
yes, all of the conditions for inference are met.

Explanation:

• Random condition: The problem states that the researcher selects a random sample of 360 babies. So, the random condition is met.
• 10% condition: Since we are not sampling from a finite population (we can assume that the number of babies born in general is much larger than 360), the 10% condition (if sampling without replacement from a finite population, \(n\leq0.1N\)) is not relevant here or can be considered met in a practical sense for inference purposes.
• Large Counts condition: For a chi - square goodness - of - fit test (which is appropriate for testing if a distribution is uniform), the expected count for each day of the week \(E=np\). Here, \(n = 360\) and \(p=\frac{1}{7}\) (since there are 7 days in a week). So, \(E=360\times\frac{1}{7}\approx51.43\geq5\). The large counts condition (all expected counts \(E\geq5\)) is met.

Answer:

Yes, all of the conditions for inference are met.