Question

A sample of 100 has a mean of 15. Assume that the population is approximately normally distributed a population standard deviation of 4. The hypothesis desired are: Ho; µ = 12.5, Ha; µ ≠ 12.5. Test the hypothesis at a level of significance of 0.02.

Answer 1

n = 100

x = 15

σ = 4

Null hypothesis H₀: μ = 12.5

Alternative hypotheses H_a: μ ≠ 15.5 (two-tailed test)

The level of significance can be considered as 0.05.

The test statistic

$Z = \frac{x - μ}{\frac{σ}{\sqrt{n}}} \\ = \frac{15 – 12.5}{\frac{4}{\sqrt{100}}} \\ = \frac{2.5 \times 10}{4} \\ = 6.25 \\ Z_{tab} = 2.33 \\ Z> Z_{tab}$

So, we reject H₀ at 2% level of significance.