IAI Actuarial Core Principles · Actuarial Statistics · Hypothesis testing and goodness of fit
A sample of n = 25 observations from a normal distribution with known standard deviation 10 has sample mean 54. Test H0: μ = 50 against H1: μ ≠ 50. What is the value of the test statistic, and what is the conclusion at the 5% level (critical value 1.96)?
The standard error is 10 divided by 5, which is 2, so z = (54 − 50)/2 = 2.0. This exceeds the two-sided 5% critical value of 1.96, so the null hypothesis that the mean is 50 is rejected.
- Az = 2.0; reject H0Correct
- Bz = 0.4; do not reject H0
- Cz = 2.0; do not reject H0
- Dz = 0.8; do not reject H0
- z = 4.0; do not reject H0
Explanation
The standard error is 10/√25 = 2. So z = (54 − 50)/2 = 2.0. Since 2.0 > 1.96, reject H0 at 5%. Using 10 as the standard error gives 0.4, which is the wrong-denominator error.
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