A researcher is studying cancer mortality rates for men in five southern states.In the five states,the sample standard deviation is 6.76 (per 100,000).A 98 percent confidence interval estimate of the population variance is represented by: A) 5(6.76)/ 13.277 and 5(6.76)/ 0.297. B) 5(6.76²)/ 13.277 and 5(6.76²)/ 0.297. C) 4(6.76)/ 13.277 and 4(6.76)/ 0.297. D) 4(6.76²)/ 13.277 and 4(6.76²)/ 0.297. E) 4(6.76²)/ 0.297 and 4(6.76²)/ 13.277.

Question

Quizplus · Accepted Answer

The formula for a confidence interval estimate of population variance is: ((n-1)*S^2)/χ^2 where n is the sample size, S is the sample standard deviation, and χ^2 is the chi-square value for the desired degree of confidence and degrees of freedom. Since the sample standard deviation is given as 6.76, we can use this value for S. We are also given that we want a 98% confidence interval, which corresponds to a chi-square value of 9.237 for 4 degrees of freedom (since we have a sample size of 5 and are estimating one population parameter). So, plugging in these values: ((5-1)*6.76^2)/9.237 = 137.588 This gives us an estimate for the population variance of approximately 137.588 (per 100,000)^2. To get the confidence interval estimate for the population variance, we can use the formula: [(n-1)*S^2/χ^2, (n-1)*S^2/χ^2] Plugging in the values: [(4*6.76^2)/9.237, (4*6.76^2)/0.297] = [129.272, 907.105] Therefore, the best choice is D) 4(6.76²)/ 13.277 and 4(6.76²)/ 0.297, since it gives the correct formula for the confidence interval estimate of population variance.

A Researcher Is Studying Cancer Mortality Rates for Men in Five