Eastwood's BA201 Assignments

Homework #15 Solutions

15.        H_o:                  H₁:

            df₁ = 21 – 1 = 20           df₂ = 18 – 1 = 17           H_o is rejected if F > 3.16

                Reject H_o.  There is more variation in selling price of ocean front homes.

 16.        H_o:                  H₁:

            df₁ = 16 – 1 = 15           df₂ = 16 – 1 = 15           H_o is rejected if F > 2.40

                      Reject H_o.  There is more variation in processing time of the new machine.

 17.        Sharkey:  n = 7              s_d = 14.79

            White:  n = 8                 s_d = 22.95

            H_o:                  H₁:

            df_s = 7 – 1 = 6               df_w = 8 – 1 = 7              H_o is rejected if F > 8.26

                  Cannot reject H_o.  There is no difference in the variation of the weekly sales.

 18.        a.         H_o:  m₁ = m₂ = m₃            H₁:  Treatment means are not all equal

            b.         a = 0.05           Reject if F > 3.89

            c.         Source             SS              df          MS           F

                        Treatment        40                2            20            4

                        Error                60               12             5

                        Total              100               14

            d.         Reject H_o.  The treatment means are not all equal.

 19.        a.         H_o:  m₁ = m₂ = m₃ = m₄                H₁:  Treatment means are not all equal

            b.         a = 0.05           Reject if F > 3.10

            c.         Source             SS              df          MS           F

                        Treatment        50                3       16.67       1.67

                        Error              200               20            10

                        Total              250               23

            d.         Do not reject H_o.

20.        Source             SS           df            MS          F

            Treatment        320            2           160       8.00

            Error                180            9             20

            Total                500          11

            a.         3

            b.         12

            c.         4.26

            d.         H_o:  m₁ = m₂ = m₃            H₁:  Not all means are equal

            e.         H_o is rejected.  The treatment means differ.

21.        H_o:  m₁ = m₂ = m₃            H₁:  Not all means are equal

            H_o is rejected if F > 3.89

            Source             SS           df            MS          F

            Treatment     63.33            2       31.667      13.38

            Error             28.40          12         2.367

            Total             91.73          14

            H_o is rejected.  There is a difference in the treatment means.

22.        H_o:  m₁ = m₂ = m₃            H₁:  Not all means are equal

            H_o is rejected if F > 3.89

            Source             SS           df            MS          F

            Treatment     26.13            2       13.065      13.52

            Error             11.60          12         0.967

            Total             37.73          14

            H_o is rejected since 13.52 > 3.89.  There is a difference in the mean weight loss among the three diets.

23.        H_o:  m₁ = m₂ = m₃ = m₄                H₁:  Not all means are equal

            H_o is rejected if F > 3.10

            Source             SS           df            MS          F

            Factor           87.79            3         29.26       9.12

            Error             64.17          20          3.21

            Total           151.96          23

            Since computed F of 9.12 > 3.10, the null hypothesis of no difference is rejected at the 0.05 level.

24.        a.         H_o:  m₁ = m₂ = m₃                        H₁:  Not all means are equal

                        H_o is rejected if F > 3.68

                        Source               SS          df          MS          F

                        Treatment       116.3          2         58.2       5.09

                        Error              171.5         15         11.4

                        Total               287.8         17

                        Reject H_o.  There is a difference in the mean scores

b.         Yes, because both endpoints are positive. 

            The mean perfectionism scores for those from a rural background differs from those with an urban background.

You may also download an EXCEL spreadsheet called anova4u.xls. It contains my solutions to various problems from the text and the EXCEL workbook related to the F-test and ANOVA.

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