Question

a doctor used to believe that babies were equally likely to be born any day of the week, but with the rise in scheduled deliveries, the doctor now claims that babies are twice as likely to be born on a weekday (monday through friday) than on a weekend (saturday and sunday). she decides to test: ( h_0: p_{\text{sun}}=\frac{1}{12}, p_{\text{mon}}=\frac{1}{6}, p_{\text{tue}}=\frac{1}{6}, p_{\text{wed}}=\frac{1}{6}, p_{\text{thu}}=\frac{1}{6}, p_{\text{fri}}=\frac{1}{6}, p_{\text{sat}}=\frac{1}{12} ) ( h_a ): not all of the ( p_i )s are as stated. she selects a random sample of 120 babies born this year and determines on which day of the week they were born. she finds that 4 were born on sunday, 24 on monday, 21 on tuesday, 18 on wednesday, 22 on thursday, 28 on friday, and 3 on saturday. the chi - square test statistic for goodness of fit is ( chi^2 = 12.95 ) and the ( p ) - value is between 0.025 and 0.05. what conclusion should she make? use ( alpha = 0.05 ). o reject ( h_0 ). there is convincing evidence that babies are twice as likely to be born on a weekday (monday through friday) than on a weekend (saturday and sunday). o reject ( h_0 ). there is convincing evidence that babies are not twice as likely to be born on a weekday (monday through friday) than on a weekend (saturday and sunday). o fail to reject ( h_0 ). there is convincing evidence that babies are twice as likely to be born on a weekday

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 $0.025$ and $0.05$, so $P - value<\alpha$. When we reject $H_0$, it means we have evidence against the claim in $H_0$. The null hypothesis $H_0$ was the claim about equal probabilities (not the new claim about babies being twice as likely on weekdays). Rejecting $H_0$ implies that the distribution is not as stated in $H_0$, which means there is evidence that the new claim (babies are not equally likely to be born each day, i.e., not as in $H_0$) is supported.

Answer:

Reject $H_0$. There is convincing evidence that babies are not twice as likely to be born on a weekday (Monday through Friday) than on a weekend (Saturday and Sunday).