Question

Are births really evenly distributed across the days of a week? Here are data on 700 births in a hospital:

Day

Sun.

Mon.

Tue.

Wed.

Thu.

Fri.

Sat.

Observed births

89

110

116

104

94

106

81

<Step 1>

Null hypothesis: the births are evenly distributed across the days of the week

Research hypothesis: the births are not equally probable on all days of the week?

<Step 2> Choose α = 5%

<Step 3> Test statistic used: χ2 =

Decision : Reject Ho if χ2 is too big.

<Step 4> Calculations and Conclusion

1˚ Arrange the data in the form of a frequency distribution (See the table above).

2˚ Obtain the expected frequency for each day.

Day

Sun.

Mon.

Tue.

Wed.

Thu.

Fri.

Sat.

Expected births

3˚ Setup a summary table to calculate the Chi-square value.

4˚ Find the degree of freedom.

5˚ Compare the calculated Chi-square value with the appropriate value from the χ2 Table.

The calculated χ2 value is

A) 7.15

B) 8.27

C) 9.26

D) 10.10

E) 11.92

F) 12.76

G) 13.68

H) 16.42

I) 19.12

J) 23.86.

Answer 1

Null hypothesis: the births are evenly distributed across the days of the week. Mathematically,

Ho: p1=p2=p3=p4=p5=p6=p7=1/7

Research hypothesis: At least one proportion is not equal to the other

Expected value = n*p = 700*1/7 = 100

Arranging the data in the table a shown and calculating the chi square value

n=700
Day	Observed, O	Probability, p	Expected, E	(O-E)2/E
Sun	89	1/7	100	1.21
Mon	110	1/7	100	1
Tue	116	1/7	100	2.56
Wed	104	1/7	100	0.16
Thu	94	1/7	100	0.36
Fri	106	1/7	100	0.36
Sat	81	1/7	100	3.61
Total	700	1	700	9.26

Chi Square is given by

= 9.26 (from the table as calculated above)

Degree of freedom = n-1 = 7-1 = 6

Chi-square value from the chi-square table, with 6 degree of freedom and alpha =0.05, it is 12.59. Since, the critical value is greater than the calculated value, we fail to reject null. Also, if we find the p-value, it is 0.159, which is greater than alpha, indicating that the result is not significant.

Conclusion

The chi-square value is 9.26 (Option C)

And the births are not evenly distributed across all days of the week