Chapter PV, Problem 3RE

(a)

To determine

To explain how many would you expect on each day if births are uniformly distributed across all days of the week.

Answer to Problem 3RE

  $10.29\text{ births}$ .

Explanation of Solution

It is given in the question that during a two-month period, $72$ babies were born at the hospital. The table in the question shows how many babies were born on each day of the week. Thus, if births are uniformly distributed across all days of the week, then the expected number of births will be calculated as:

  $\begin{array}{l}E(x)=\frac{7+17+8+12+9+10+9}{7}\\ =10.29\text{ births}\end{array}$

(b)

To determine

To explain does this indicate that women might be less likely to give birth on a Monday.

Answer to Problem 3RE

This does not indicate that women might be less likely to give birth on a Monday.

Explanation of Solution

It is given in the question that during a two-month period, $72$ babies were born at the hospital. The table in the question shows how many babies were born on each day of the week. As only seven births occur on a Monday, then we can say that,

  $\begin{array}{l}SE\text{(}{p}_1-p_2\text{)=}\sqrt{\frac{(\frac{1}{7})(\frac{6}{7})}{\Sigma x}}\\ =0.041\\ \text{with }\Sigma \text{x}=72\\ z=\frac{\frac{7}{\Sigma x}-\frac{1}{7}}{0.041}\\ =-1.1\end{array}$

Thus, from this we can conclude that $z=-1.1$ is unremarkable therefore this does not indicate that women might be less likely to give birth on a Monday.

(c)

To determine

To explain are the $17$ births on Tuesdays unusually high.

Answer to Problem 3RE

Yes, it is.

Explanation of Solution

It is given in the question that during a two-month period, $72$ babies were born at the hospital. The table in the question shows how many babies were born on each day of the week. Since there are $17$ births on Tuesdays, therefore we have,

  $\begin{array}{l}z=\frac{\frac{17}{\Sigma x}-\frac{1}{7}}{0.041}\\ =2.26\end{array}$

Thus, the P-value for two-tailed test is from the tables is $0.024$ and therefore a low probability on chance alone. Thus, yes, the $17$ births on Tuesdays are unusually high.

(d)

To determine

To explain can you think of any reasons why births may not occur completely at random.

Explanation of Solution

It is given in the question that during a two-month period, $72$ babies were born at the hospital. The table in the question shows how many babies were born on each day of the week. Thus, birth scheduling or induced labor may be the reasons why births may not occur completely at random because some births are scheduled for the convenience of the doctor or the mother.