Question

Randomly selected birth records were​ obtained, and categorized as listed in the table to the right. Use a

0.01

0.01 significance level to test the reasonable claim that births occur with equal frequency on the different days of the week. How might the apparent lower frequencies on Saturday and Sunday be​ explained?

Day nbsp Day	Sun	Mon	Tues	Wed	Thurs	Fri	Sat
Number of Births Number of Births	48 48	64 64	61 61	60 60	56 56	65 65	47 47

Determine the null and alternative hypotheses.

H0​: (choose one)

1. At least one day has a different frequency of births than the other days.
2. Births occur with the same frequency on the different days of the week.
3. Births occur with all different frequencies on the different days of the week.
4. At least two days have a different frequency of births than the other days.

H1​: (choose one)

1. At least one day has a different frequency of births than the other days.
2. Births occur with the same frequency on the different days of the week.
3. Births occur with all different frequencies on the different days of the week.
4. At least two days have a different frequency of births than the other days.

Calculate the test​ statistic, χ2 = _____

​(Round to three decimal places as​ needed.)

Calculate the​ P-value.

​P-value = _____

​(Round to four decimal places as​ needed.)

What is the conclusion for this hypothesis​ test?

A. Fail to reject H0. There is sufficient evidence to warrant rejection of the claim that births occur with equal frequency on the different days of the week.

B.

Fail to reject H0. There is insufficient evidence to warrant rejection of the claim that births occur with equal frequency on the different days of the week.

C.

Reject H0. There is sufficient evidence to warrant rejection of the claim that births occur with equal frequency on the different days of the week.

D.

Reject H0. There is insufficient evidence to warrant rejection of the claim that births occur with equal frequency on the different days of the week.

How might the apparent lower frequencies on Saturday and Sunday be​ explained?

A.

Induced or​ Caesarean-section births are scheduled during the week whenever possible.

B.

Induced or​ Caesarean-section births are scheduled on weekends whenever possible.

Answer 1

Null Hypotheses, H0​:

Births occur with the same frequency on the different days of the week.

Alternative Hypothesis, H1:

At least one day has a different frequency of births than the other days.

Day	O: Observed	E: Expected	(O-E)2/E
Sun	48	401/7 =57.28571429	1.505165657
Mon	64	57.28571429	0.786961168
Tues	61	57.28571429	0.240826505
Wed	60	57.28571429	0.128607054
Thurs	56	57.28571429	0.02885643
Fri	65	57.28571429	1.038831493
Sat	47	57.28571429	1.846811542
Total	401	401	5.576

$\chi^2$ =$\Sigma \ [(O-E)^2/E]$ =5.576

P-value for Chi-square test statistic of 5.576 at n-1 =7-1 =6 degrees of freedom is: P-value =0.4723

Conclusion: Since, P-value is greater than the significance level of 0.01 (i.e., 0.4723 > 0.01), we fail to reject the null hypothesis(H0) at 0.01 significance level.

Thus, the correct option is B. Fail to reject H0. There is insufficient evidence to warrant rejection of the claim that births occur with equal frequency on the different days of the week.

The apparent lower frequencies on Saturday and Sunday might be explained as:

B.

Induced or​ Caesarean-section births are scheduled on weekends whenever possible.

Therefore, the number of births on Saturdays and Sundays are less as the Caesarean-section births are less common (about 1 in 3) and the number of births during the other days of the week are relatively more.