Question

A doctor believes that the proportions of births in this country on each day of the
week are equal. A simple random sample of 700 births from a recent year is
selected, and the results are below. At significance level of 0:01, is there enough
evidence to support the doctor's claim? (Use Chi Test)
​

Answer 1

Answer:

Day Sunday Monday Tuesday Wednesday Thursday Friday Saturday

Frequency 65 103 114 116 115 112 75

(i) The null hypothesis H0:the population frequencies are equal to the expected frequencies

(to be calculated below).

(ii) The alternative hypothesis, Ha: the null hypothesis is false.

(iii) α = 0.01.

(iv) The degrees of freedom: k − 1 = 7 − 1 = 6.

(v) The test statistic can be calculated using a table:

Step-by-step explanation:

Day E O O − E (O − E)

2 (O−E)

2

E

Sunday 700/7 = 100 65 −35 1225 12.25

Monday 700/7 = 100 103 3 9 0.09

Tuesday 700/7 = 100 114 14 196 1.96

Wednesday 700/7 = 100 116 16 256 2.56

Thursday 700/7 = 100 115 15 225 2.25

Friday 700/7 = 100 112 12 144 1.44

Saturday 700/7 = 100 75 −25 625 6.25

χ

2 =

X ( observed − expected )2

expected =

X (O − E)

2

E

= 26.8.

(vi) From α = 0.01 and k − 1 = 6, the critical value is 16.812.

(vii) Is there enough evidence to reject H0? Since χ

2 ≈ 26.8 > 16.812, there is enough

statistical evidence to reject the null hypothesis and to believe that the proportion of

births is not the same for each day of the week.