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, he selects a random sample of 350 babies and records on which day of the week they were born. he finds that 28 babies were born on sundays, 65 on mondays, 48 on tuesdays, 56 on wednesdays, 45 on thursdays, 62 on fridays, and 46 on saturdays. he tests the following 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. the chi - square test statistic is ( chi^2 = 18.68 ) and the p - value is between 0.0025 and 0.005. what conclusion should the researcher make? use ( alpha = 0.05 ). reject ( h_0 ). there is convincing evidence that the distribution of births is not uniform across the days of the week. reject ( h_0 ). there is not convincing evidence that the distribution of births is not uniform across the days of the week. fail to reject ( h_0 ). there is convincing evidence that the distribution of births is not uniform across the days of the week. fail to reject ( h_0 ). there is not convincing evidence that the distribution of births is not uniform across the days of the week.

Explanation:

In hypothesis testing, if the P - value is less than the significance level ($\alpha$), we reject the null hypothesis ($H_0$). Here, $\alpha = 0.05$ and the P - value is between $0.0025$ and $0.005$. Since $0.0025\lt0.05$ and $0.005\lt0.05$, we reject $H_0$. When we reject $H_0$, it means there is convincing evidence against $H_0$. The null hypothesis claims that the distribution of births is uniform across the days of the week, so rejecting $H_0$ implies there is convincing evidence that the distribution of births is not uniform across the days of the week.

Answer:

Reject $H_0$. There is convincing evidence that the distribution of births is not uniform across the days of the week.