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Q- Search Sheet Insert Page Layout Formulas Data Review View Developer Arial -insert . .A DeleteZ Formating as Table StylesFortFi 5 problems Problem Co stud 80%, 90%, and 95% oofdence intervals for ro mean of his data 6.11383372 1221679045 12.54830756 11.77001117 9.905112875 14 888567 1143743988 68563846 838637434 10.554782 10.121269 122995907 144705887 16.71547826 1393784335 14.11894487 151012868 11.76756143 7.786938153 7317429767 10.16603397 1108819674 6.596124654 1140694938 10.4 10.49983291 12.59209646 1593683421 11.1622107 2 86292433 9.62952894 15.05779943 1227691305 11.62291349 13.56349149 12 8524 93 14.86431774 14.6889657 16.51114988 413674637 11.33574022 11.10582318 10.67265639 3.36174883 16.61404432 853601712 15.14525452 1.15134392 13.58139079 371202535 6 13 14 15 16 Problem 2 18 Construct 8%, 90%, and 96%Cofidence nervals for Pe mean of this data 12.27691305 4.6889557 16.51114988 15.05779943 358139079 8.667948387 12 1.62291349 1356349149 12.66292433 8853601712 1 5.14525452 1.15134392 12.85249293 14.86431774 371202535 6876353718 9.073732817 1 2 Problem 3 Corwruct eonnard 95% Confeserce riarvals lortheanerences in the means of XanY

Explanation / Answer

ANSWER TO PROBLEM 1:

To calculate 80%, 90% and 95% confidence interval (CI) for the given data

(a)80%

For 80%

#step 1: Find

               = 1-0.8 = 0.2

              /2 = 0.1

       total number, n = 54

      #step 2: Formula for confidence interval

        Since the sample size, 54> 30, i.e., the sample is large

                Therefore, The formula for confidence interval is :

                 ± E ,

where E = z2(/n)

                    where, is the sample mean (here we are given the population so, we will use population mean) is the population standard deviation and n is the total size of sample (in this case population)

#step 3: Calculate the required values from given data

            calculating from the formula ,

                = a/n = 633.873095561/54

              we get = 11.738390658537

               and = [ (a - mean)2 / n ]

                    = 2.7355064448214

#step 4: Calculate the confidence interval

                 substituting above values in E

                      E = z0.1(2.7355064448214/54)              z0.1 = 1.28(from cumulative probability distribution table)

                                      E= 1.28 * 0.372255277

                                        E = 0.476486754

                                         Hence, the confidence interval is (11.73830658537 ± 0.476486754)

                                        i.e., (11.2619039,12.2148774)

similarly,

For 90%

#step 1: Find

               = 1-0.9 = 0.1

              /2 = 0.05

total number, n = 54

#step 2: Formula for confidence interval

                   Since the sample size, 54> 30, i.e., the sample is large

                Therefore, The formula for confidence interval is :

                    ± E ,

               where E = z2(/n)

                          where, is the sample mean (here we are given the population so, we will use population mean)   is the population standard deviation and n is the total size of sample (in this case population)

#step 3: Calculate the required values from given data

            calculating from the formula ,

                = a/n = 633.873095561/54

              we get = 11.738390658537

               and = [ (a - mean)2 / n ]

                    = 2.7355064448214

#step 4: Calculate the confidence interval

                 substituting above values in E

                      E = z0.05(2.7355064448214/54)              z0.01 = 1.645(from cumulative probability distribution table)

                                      E= 1.645 * 0.372255277

                                        E = 0.612355806

                                         Hence, the confidence interval is (11.738390658537 ± 0.612355806)

                                        i.e., (11.12603484,12.35074646)

similarly,

For 95%

#step 1: Find

               = 1-0.95 = 0.05

              /2 = 0.025

total number, n = 54

#step 2: Formula for confidence interval

                   Since the sample size, 54> 30, i.e., the sample is large

                Therefore, The formula for confidence interval is :

                    ± E ,

where E = z2(/n)

                          where, is the sample mean (here we are given the population so, we will use population mean)   is the population standard deviation and n is the total size of sample (in this case population)

#step 3: Calculate the required values from given data

            calculating from the formula ,

                = a/n = 633.873095561/54

              we get = 11.738390658537

               and = [ (a - mean)2 / n ]

                    = 2.7355064448214

#step 4: Calculate the confidence interval

                 substituting above values in E

                      E = z0.025(2.7355064448214/54)              z0.025 = 1.96(from cumulative probability distribution table)

                                      E= 1.96 * 0.372255277

                                        E = 0.729620342

                                         Hence, the confidence interval is (11.738390658537 ± 0. 729620342)

  i.e., (11.00877031,12.46801099)

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