Question

A sample of 400 individuals is found to have a mean height of 67.47 inches. Can it be reasonably regarded as a sample from a large population with a mean height of 67.39 inches and standard deviation of 1.30 inches?

Answer 1

Given Sample size n = 400 

Sample mean = 67.47 

The population mean µ = 67.39 

Population SD σ = 1.3 

Null hypothesis H₀ : µ = 67.39 inches 

(the sample has been drawn from the population with mean heights 67.39 inches)

Alternative hypothesis H₁ : µ ≠ 67.39 inches 

(the sample has not been drawn from the population with mean height 67.39 inches) 

The level of significance α = 5% = 0.05

Test statistic

The significant value or table value Z_α/2= 1.96. We see that 1.2308 < 1.96 (i.e) Z <  Z_α/2. Since the calculated value is less than the table value at 5% level of significance, the null hypothesis is accepted. Hence we conclude that the data do not provide us with any evidence against the null hypothesis. Thus, the sample has been drawn from a large population with a mean height of 67.39 inches and S.D 1.3 inches.