Question

Among 400 randomly -selected persons of a city, 280 like icecream. Test at 1% level of significance that 50% of the people in that city like ice-creams.

Answer 1

Linking ice-cream is an attribute, so use test for proportion. 

Given: n = 400, x = 280 (ice cream liked)

∴ Sample proportion : p  \(\frac{x}{n}\)= \(\frac{280}{400}\) and

P₀ = 0.5 (50% people like ice cream): α = 1%

H₀: 50% people like ice cream (i.e., P₀ = 0.5)

H₁ : people liking ice cream differ from 50% (i.e., P₀ ≠ 0.5 ) {two tailed test ±K) under H₀ the test statistic is :

At α = 1% the two tail crtical values are ±K = ± 2.58

Here Z_cal lies in Rejection Region (R.R)

∴ H₀ is rejected and H₁ is aceepted.

conclusion: P₀ ≠ 0.5 : people liking ice cream differ from 50%.