Question

The table below shows the frequencies for the days of the weeks that prospective mothers were admitted to a hospital to give birth. A physician claims that because many births are induced or involve cesarean​ section, they are scheduled for days other than Saturday or​ Sunday, so births do not occur on the seven different days of the week with equal frequency. Use a

0.010.01

significance level to test that claim.

Day nbspDay	Sun	Mon	Tues	Wed	Thurs	Fri	Sat
Number of BirthsNumber of Births	4848	5656	6161	6565	6060	5757	4848

Determine the null and alternative hypotheses.

Upper H 0H0​:

▼

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

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.

Upper H 1H1​:

▼

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

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.

Births occur with all different frequencies 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.

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.

B.

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.

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 on weekends whenever possible.

B.

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

Answer 1

Solution:

Determine the null and alternative hypotheses.

H0​: Births occur with the same frequency on the different days of the week.

H1​: Births occur with all different frequencies on the different days of the week.

Calculate the test​ statistic,

$\boldsymbol{\chi^{2}=4.425 }$

Explanation:

(0-E)? Expected E Number of Births Number of Births O Day Sun 48 56.42857 1.258951 Mon 56 56.42857 0.003255 Tues 61 56.42857 0.370344 Wed 65 56.42857 1.301989 Thurs 0.22604 60 56.42857 Fri 57 56.42857 0.005787 48 56.42857 Sat 1.258951 (0-E)? Σ = 4.425316 Total 395 395 (0-E) Σ-ΣΟΕ -= 4.425 p- value = P( > 4.425) = 0.6193

Calculate the​ P-value.

$\boldsymbol{p=value=0.6193 }$

What is the conclusion for this hypothesis​ test?

D. 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.

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

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