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A doctor claims that the number of births by day of the week is uniformly distributed....

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Statistics

A doctor claims that the number of births by day of the week isuniformly distributed. To test this claim, you randomly select 700births from a recent year and record the day of the week on whicheach takes place. The table shows the results.

Day:SundayMondayTuesdayWednesdayThursdayFridaySaturday
Births:68(100)107(100)117(100)110(100)114(100)109(100)75(100)

Test the doctor's claim at the significance level a=0.05.

a) What is the assumed proportion of births in each day?(infractions)

b) State H0 and Ha.

c) What is the degrees of freedom of the test?

d) Calculate the x^2 test statistic.

e) Decide whether to reject the null hypothesis.

g) Interpret the decision in the context of the originalclaim.

Answer & Explanation Solved by verified expert
4.4 Ratings (859 Votes)

a)

assumed proportion of births in each day =1/7

b)

Ho: births by day of the week is uniformly distributed

Ha: births by day of the week is not uniformly distributed

c)

degree of freedom =categories-1= 6

d)

applying chi square goodness of fit test:
           relative observed Expected residual Chi square
category frequency(p) Oi Ei=total*p R2i=(Oi-Ei)2/Ei
Sun 1/7 68.0 100.00 10.240
Mon 1/7 107.0 100.00 0.490
Tue 1/7 117.0 100.00 2.890
Wed 1/7 110.0 100.00 1.000
Thu 1/7 114.0 100.00 1.960
Fri 1/7 109.0 100.00 0.810
Sat 1/7 75.0 100.00 6.250
total 1.000 700 700 23.6400
test statistic X2 = 23.64

e)

for 0.05 level and 6 df :crtiical value X2 = 12.592
Decision rule: reject Ho if value of test statistic X2>12.592
since test statistic falls in rejection region we reject null hypothesis

g)

we have sufficient evidence to conclude that  births by day of the week is not uniformly distributed
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