Question

The cholesterol levels of adult males are approximately normally distributed with a mean of 224 mg/dl, and a variance, o', of 521. Some researchers claim that the variance of cholesterol levels of adult males is less than 521. A sample of 15 adult males' blood tests had a mean of 222.5 mg/dL and a variance of 192. Is there enough evidence to conclude, at the 0.05 level of significance, that the variance of cholesterol levels of adult males is less than 5217 Perform a one-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. р 0 P The null hypothesis X S The alternative hypothesis: 020 D=0 OSO The type of test statistics (Choose one)

Answer 1

As we are testing here whether the variance is less than 521 or not, therefore the null and the alteranative hypothesis here are given as:

H: 02 = 521

As we are testing for variance here, this is a chi square test here. Therefore chi square test statistic is to be used here.

The test statistic here is computed as:

x² = (n-1)s o (15 – 1)192 521 = 5.159

Therefore 5.159 is the test statistic value here.

For 0.05 level of significance and 14 degrees of freedom, as this is a one tailed test, we have from chi square distribution tables here:

P(Xi4 > 23.685) = 0.05

Therefore 23.685 is the required critical value here.

As the test statistic value here is less than the critical value, therefore it lies in the non rejection region here. Therefore we cannot support the claim here that the variance is less than 521. Therefore No is the correct answer here.