A and B Eat your cereal: Boxes of cereal are labeled as containing 14 ounces. Following are the weights, in ounces, of a sample of 16 baxes. It is reasonable to assumethat the population is approximately normal.14.07 13.98 14.16 14.17 14.11 14.03 14.16 13.98.14.06 14.05 14.12 14.13 14.19 14.17 14.05 14.04Send data to ExcelO ER (a) Construct a 95% confidence interval for the mean weight. Round the answers to at least three decimal places.A 95% confidence interval for the mean weight isPart: 1/2Part 2 of 2(b) The quality control manager is concerned that the mean weight is actually less than 14 ounces. Based on the confidence interval, is there a reason tobe concermed? Explain.The quality control manager should (Choose one) concerned that the mean weight is actually less than 14 ounces.benot be

Given data : 14.07 13.98 14.16 14.17 14.11 14.03 14.16 13.98 14.06 14.05 14.12 14.13 14.19 14.17 14.05 14.04solution : From the above given data Sample Size, n = 16 Sample Mean, x̄ = 14.091875 sample standard deviation, s = 0.06843184 confidence level,c=0.95 Significance level, α =1-0.95 = 0.05 Degree of freedom df = n-1 = 15 critical value : critical value at α=0.05 and df=15 is tα/2,df=2.131 .....from student's t distribution table 95% confidence interval =14.091875 ± 2.131 x 0.06843184/√16 =14.091875 ± 0.036457 =( 14.091875 - 0.036457 , 14.091875 + 0.036457 ) = ( 14.055 , 14.128 ) 95% confidence interval is 14.055<u<14.128b) since Confidence interval does not contain hypothesize mean value so we reject the null hypothesis therefore The quality control manager should be concerned that the mean weight is actually less than 14 ounces.