Question

In a sample of 500 people in Rajastan , 280 are rice eaters
and the rest are wheat eaters. can we assume that both rice and
wheat are equally popular in this district at 1% level of significance?

Answer 1

n = 500

p = sample proportion of rice eaters

p= 280/500=0.56

P = population proportion of rice eaters

P= 1/2 = 0.5

Q =1-P=1-0.5=0.5

Null hypothesis

Both rice and wheat eaters are equally popular in the state

H₀ : P=0.5

Alternative hypothesis H₁: P $\not =$ 0.5

(two tailed test)

z=(p-P)/ $\sqrt{\frac{P*Q}{n}}$ =(0.56-0.5)/$\sqrt{\frac{0.5*0.5}{500}}$ =2.68

The calculated value of z=2.68

The tabulated value of z at 1% level of significance for two-tailed test is 2.58.

Since calculated z> tabulated z, we reject the Null Hypothesis H₀ at 1% level of significance and conclude that rice and wheat are not equally popular in the district