Question

You are testing a batch of pills. The manufacturer claims that the standard deviation of their weights is less than 0.1 mg. You test ten of them, with weights in mg of 50.11, 49.87, 49.99, 50.02, 50.04, 49.92, 49.95, 50, 50.01, 50.09. Assume a normal distribution for the population, and evaluate the claim at the 99% confidence level.

1) what is H1 and H0

2)what is the result of the statistical test (Examples: "The p-value was 0.061" or "the upper bound of the population mean was 12.4g")

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: σ = 0.1
Alternative Hypothesis, Ha: σ ≠ 0.1

Test statistic,
Χ^2 = (n-1)*s^2/σ^2
Χ^2 = (10 - 1)*0.0732^2/0.1^2
Χ^2 = 4.822

P-value Approach
P-value = 0.1505

As P-value >= 0.01, fail to reject null hypothesis.

The standard deviation is not less than 0.1 mg