Question

A physician wants to test if the variance in cholesterol levels of adult men in a certain laboratory equals to 100 (H0 : σ2 = 100 versus H1: σ2 < 100). A random sample of cholesterol levels from 25 adult males from this laboratory produced a sample standard deviation of 12. Test the physician’s claim at 5% level of significance.

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis H₀: σ² = 100

Alternative hypothesis H_A: σ² < 100

Formulate an analysis plan. For this analysis, the significance level is 0.05.

Analyze sample data. Using sample data, the degrees of freedom (DF), and the test statistic (X²).

DF = n - 1 = 25 -1

D.F = 24

We use the Chi-Square Distribution Calculator to find P(Χ² > 34.56) = 0.075

Interpret results. Since the P-value (0.075) is greater than the significance level (0.05), we have to accept the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that the variance in cholesterol levels of adult men in a certain laboratory equals to 100.