Question

The diameters n inches) of 17 randomly selected bolts produced by a machine are listed. Use a 90% level of confidence to construct a confidence interval for population variance ơ2 and (b) the population standard deviation ơ. Interpret the results. a the 4.481 4411 4003 4329 4004 3797 3806 3.775 4 223 3.986 4.153 4.565 3938 3.753 3.865 3.814 4.457 () The confidence interval for the population variance is (Round to three decimal places as needed.)

Answer 1

Given data {4, 481, 4, 411, 4.003, 4.004, 3.797, 3.806, 3.775, 4.223, 3.986, 4.153, 4.565, 3.938 3.753, 3.865, 3.814, 4.457} sample size n = 17 Mean of give sample X^bar = sigma xi/n = 4.08 variance s^2 = sigma (x_1 - x^bar)^2/n - 1 = 0.078 to find 90% confidence interval, level of significance alpha = 0.10 x^2_alpha/2 critical value at n - 1 (160 degrees of freedom = 26.30 x^2_alpha/2 critical value at n - 1 (16) degrees of freedom = 7.96 90% CI for variance is (n - 1) s^2/x^2_alpha/2 lessthanorequalto a^2 lessthanorequalto (n- 1)s^2/x^2_1 - alpha/2 (17 - 1) 0.078/26.30 lessthanorequalto a^2 lessthanorequalto (17 - 1) s^2/x^2_1 - alpha/2 (17 - 1) 0.078/26.30 lessthanorequalto sigma^2 lessthanorequalto (17 - 1) 0.078/7.96 0.0475 lessthanorequalto a^2 lessthanorequalto 0.1568 90% CI for standard deviations is squareroot (n- 1) s^2/x^2_alpha/2 lessthanorequalto sigma lessthanorequalto squareroot (n - 1) s^2/x^2 _ 1 - alpha/2 squareroot (17 -) 0.078/26.30 lessthanorequalto sigma lessthanorequalto (17 - 1) 0.078/7.96 0.2179 lessthanorequalto sigma lessthanorequalto 0.3959