You randomly select and measure the contents of 10 bottles of cough syrup. The r

Question

You randomly select and measure the contents of 10 bottles of cough syrup. The results (in fluid ounces) are shown. 4.215 4.294 4.255 4.243 4.184 4.212 4.265 4.241 4.222 4.231 Assume the sample is taken from a normally distributed population. Construct 99% confidence intervals for (a) the population variance sigma^2 and (b) the population standard deviation sigma. (a) The confidence interval for the population variance is (Round to six decimal places as needed.) b) The confidence interval for the population standard deviation is (Round to four decimal places as needed.)

Explanation / Answer

Sample variance calculated will be = 0.000954

Critical value of chi square distribution at 0.01 level and df = 10-1 =9 are 1.734933, 23.58935

Confidence Interval for population variance

(9*0.000954/23.58935, 9*0.000954/1.734933)

( 0.000364, 0.004946)

Confidence Interval for population Standard deviation

(Sqrt(0.000364), Sqrt(0.004946))

(0.0703, 0.0191)

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