sample mean for data set

Question

The sample mean for a data set is 0.1315, where n = 112 and s = 16.70. Find the test statistic for the claim: 𝜇 > 0.10.

Express to 3 decimal places.

Answer 1

State null and alternate hypotheses

H₀: µ≤0.10

H_a: µ>0.10

Calculate z-statistic

Z = (x̄-µ)/(s/√n)

Z = (0.1315-0.10)/(16.70/√112)

Z ≈ 0.020

Calculate p-value

P(Z>0.02) = 1 - 0.5080 = 0.492

Assuming a significance level of α=0.05, since 0.492>α, we fail to reject the null hypothesis. Thus, we are 95% confident that the true population mean is less than or equal to 0.10

Hope this helped! The answer in bold is the test-statistic.