Question

10. Suppose that an extensive study found that the weight loss in pounds after following a certain diet is normal with σ= 5.7 pounds. A new modification of the diet has been implemented and a random sample of 21 people use the modified diet for 6 months. For these people, the sample standard deviation of weight loss is 4.1 pounds. Does this result indicate that the variance of the weight loss for the modified diet is different? Use a significance level of 0.01.

Answer 1

H₀: $\sigma^2$ = (5.7)²

H₁: $\sigma^2 \neq$ (5.7)²

The test statistic $\chi^2$ = (n - 1)s²/$\sigma^2$

= 20 * (4.1)^2/(5.7)^2

= 10.35

At alpha = 0.01, the critical values are $\chi^2 _{0.005, 20}$ = 7.4338

   = 39.9968

X0.995,20

Since the test statistic value lies between the critical values (7.4338 < 10.35 < 39.9968), so we should not reject the null hypothesis.

At 0.01 significance level there is not sufficient evidence to conclude that the variance of the weight loss for the modified diet is different.