Question

at the α = 0.05 significance level test the claim that a population has a standard deviation of 20.3. a random sample of 18 people yields a standard deviation of 27.1.

Answer 1

To test the claim that a population has a standard deviation of 20.3, use a chi-square test.

Step-by-step explanation:

To test the claim that a population has a standard deviation of 20.3, we can use a chi-square test. In this case, since we are given sample data, we can calculate the chi-square test statistic using the formula:

χ² = (n-1) * s² / σ²

Where χ² is the chi-square test statistic, n is the sample size, s is the sample standard deviation, and σ is the population standard deviation. Plugging in the values from the problem, we get:

χ² = (18-1) * (27.1)² / (20.3)²

Calculating this expression will give us the chi-square test statistic. We can then compare this value to the critical value from the chi-square distribution at a 0.05 significance level with the appropriate degrees of freedom (n-1). If the calculated chi-square test statistic is greater than the critical value, we reject the claim that the population has a standard deviation of 20.3. Otherwise, we do not have enough evidence to reject the claim.