Answer to Question #127195 in Statistics and Probability for mimi

Question

Life expectancy Religion A Religion B Religion C No Religion
> 90 years old 27 26 18 29
Take α= 0.05.
H0 : PA = PB = PC = PNO RELIGION = .25
H1 : PA ≠ PB ≠ PC ≠ PNO RELIGION ≠ .25
a. What is the critical value of the chi-square?
b. What is the degree of freedom?
c. What is the value of the test statistics of the chi-square?
d. What is the p-value?
e. Can we conclude that the life expectancy of the Malaysian men depends on their religious affiliation? State your reason.

Answer 1

a. Critical value for $\alpha=0.05,\;df=3:\;\chi^2=7.81.$

b. Degrees of freedom: $df=n-1=4-1=3.$

c. test statistic: $\chi^2=\frac{(27-25)^2}{25}+\frac{(26-25)^2}{25}+\frac{(18-25)^2}{25}+\frac{(29-25)^2}{25}=2.8.$

d. P-value: $p=0.4235.$

e. Since the p-value is greater than 0.05, fail to reject the null hypothesis.

There is not enough evidence to conclude that the life expectancy of the Malaysian men depends on their religious affiliation.