Construct a 99% confidence interval for the population variance and standard deviation, given a sample size of 30 and a sample standard deviation of 1.2 mg.

Fresh day kwambokaagnes, let's solve. b) i) 99% Confidence Interval for Population Variance (^2) Step 1: Identify the given information. Sample size, n = 30 Sample standard deviation, s = 1.2 mg Sample variance, s^2 = (1.2)^2 = 1.44 mg^2 Confidence level = 99%, so = 1 - 0.99 = 0.01 Degrees of freedom, df = n-1 = 30-1 = 29 Step 2: Determine the critical chi-squared values. For a 99% confidence interval with df = 29: ^2_1-/2, df = ^2_1-0.01/2, 29 = ^2_0.995, 29 = 13.121 ^2_/2, df = ^2_0.01/2, 29 = ^2_0.005, 29 = 52.336 Step 3: Calculate the confidence interval for the population variance. The formula for the confidence interval for population variance is: ((n-1)s^2)/(^2_/2, n-1) < ^2 < ((n-1)s^2)/(^2_1-/2, n-1) Substitute the values: ((30-1)(1.44))/(52.336) < ^2 < ((30-1)(1.44))/(13.121) (29 × 1.44)/(52.336) < ^2 < (29 × 1.44)/(13.121) (41.76)/(52.336) < ^2 < (41.76)/(13.121) 0.79809 < ^2 < 3.18268 Rounding to three decimal places: 0.798 mg^2 < ^2 < 3.183 mg^2 b) ii) 99% Confidence Interval for Population Standard Deviation () Step 1: Use the confidence interval for population variance from b) i). The confidence interval for population standard deviation is found by taking the square root of the confidence interval for the population variance: sqrt(0.79809) < < sqrt(3.18268) 0.89336 < < 1.78399 Rounding to three decimal places: 0.893 mg < < 1.784 mg c) Interpretation of Findings in b(i) and b(ii) • For the population variance: We are 99% confident that the true population variance of the weights of the allergy medicine is between 0.798 mg^2 and 3.183 mg^2. • For the population standard deviation: We are 99% confident that the true population standard deviation of the weights of the allergy medicine is between 0.893 mg and 1.784 mg. This means that if we were to repeat this sampling process many times, 99% of the confidence intervals constructed would contain the true population standard deviation. Send me the next one 📸