Question

Solve the problem with complete solution.

Problem:A survey was conducted to determine whether sex and age are related among

stereo shop customers. A total of 200 respondents was taken and the results are

presented below.

Age Male Female Total

Male 60 50 110

Female 80 10 90

Total 140 60 200

Instruction: Conduct a test whether sex and age of stereo shop customers are

independent at 1% level of significance.

Answer 1

We need to use Chi-square test:

H₀: sex and age are independent, H₁: sex and age are dependent.

O - observed value

E (expected value) = (row sum*column sum)/200

Let's place the expected values in the corresponding cells along with the observed values:

$\chi^2$(test value) = $\sum\frac{(O-E)^2}{E}=\frac{(60-77)^2}{77}+\frac{(80-63)^2}{63}+\frac{(50-33)^2}{33}+\frac{(10-27)^2}{27}=27.80$

R - number of rows

C - number of columns

d.f. = (R-1)(C-1) = 1*1 = 1

critical value ($\alpha=0.01$, d.f.=1, right-tailed test) = 6.64

The decision is to reject the null hypothesis since 27.80>6.64

Sex and age of stereo shop customers are dependent.