Question

Boys of a certain age are known to have a mean weight of 85 pounds. A complaint is made that the boys living in hostels are underfed. So a sample of 25 boys are weighed and ‘ found to have a mean weight of 80.94 pounds. The population S.D is 11.6. What should be concluded about the complaint?

Answer 1

Given n = 25, µ = 85, \(\overline{x}\) = 80.94, and σ = 11.6 

Null hypothesis H₀ : µ = 85 (the boys are not underfed) 

Alternative hypothesis H₁ : µ < 85 (the boys are underfed) 

Test statistic:

Let us take the significance level α = 0.05. The table value is Zα = -1.645

Now -1.75 < -1.645 (i.e) Z < Zα . Therefore we reject the null hypothesis. Since the calculated value falls in the rejection region. Hence we conclude that the boys are underfed. So the complaint should be addressed immediately.