Question

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

0.010.01

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 nbspDay	Sun	Mon	Tues	Wed	Thurs	Fri	Sat
Number of BirthsNumber of Births	4545	6565	6161	6060	6161	5757	4444

Determine the null and alternative hypotheses.

Upper H 0H0​:

▼

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

Births occur with all different frequencies on the different days of the week.

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

At least two days have a different frequency of births than the other days.

Upper H 1H1​:

▼

Births occur with all different frequencies on the different days of the week.

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

At least two days have a different frequency of births than the other days.

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

Calculate the test​ statistic,

chi squaredχ2.

chi squaredχ2equals=nothing

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

Calculate the​ P-value.

​P-valueequals=nothing

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

What is the conclusion for this hypothesis​ test?

A.

RejectReject

Upper H 0H0.

There is

sufficientsufficient

evidence to warrant rejection of the claim that births occur with equal frequency on the different days of the week.

B.

Fail to rejectFail to reject

Upper H 0H0.

There is

sufficientsufficient

evidence to warrant rejection of the claim that births occur with equal frequency on the different days of the week.

C.

RejectReject

Upper H 0H0.

There is

insufficientinsufficient

evidence to warrant rejection of the claim that births occur with equal frequency on the different days of the week.

D.

Fail to rejectFail to reject

Upper H 0H0.

There is

insufficientinsufficient

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

The statistical software output for this problem is:

Hence,

Hypotheses:

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

H1: At least one day has a different frequency of births than the other days.

Test statistic = 7.354

P-value = 0.2894

Conclusion: Option D is correct.

How might the apparent lower frequencies on Saturday and Sunday be​ explained? Option A is correct.