Answer to Question #113237 in Statistics and Probability for Avinash Kumar

Question

In a sample of 1000 people in Ambedkar Nagar, 540 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 = 1000

p = sample proportion of rice eaters

p= 540/1000

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)/ $\sqrt{\frac{P*Q}{n}}$ =(0.54-0.5)/$\sqrt{\frac{0.5*0.5}{1000}}$ =2.53

The calculated value of z=2.53.

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

Since calculated z< tabulated z, we accept the Null Hypothesis H₀ at 1% level of significance and conclude that both rice and wheat are equally popular in the district