Question

  For the following Minitab outputs,

     (i) name the test used

    (ii) state Ho and Ha

   (iii) conduct the test at a = .05 (identify and use the P-value if  it is available.)

(a)  MTB > ttes A c3;    

    SUBC> alte -1.

    Test of mu = A vs mu < 0

    Variable     N      Mean    StDev   SE Mean         P‑Value

    C3         200    3.8300   0.5403    0.0310         0.90

      (i) Name: __________________________________

     (ii) Ho: _________________ ,                                          Ha : _________________

    

    (iii)                              

                                                               

(b)       MTB > let c3=c2‑c1

     MTB > wtes 0 c3;

     SUBC> alte ‑1.

     TEST OF MEDIAN = 0.000000 VERSUS MEDIAN L.T. 0.000000

                     N FOR   WILCOXON           ESTIMATED

                  N   TEST  STATISTIC  P‑VALUE     MEDIAN

     C3          28     28       82.0    0.003     ‑22.00

      (i) Name: __________________________________

     (ii) Ho: _________________ ,                                       Ha : _________________

    

    (iii)                              

                                                         

(c) MTB > krusk c5 c6

    LEVEL    NOBS    MEDIAN  AVE. RANK   Z VALUE

        1       5     5.600        9.5     ‑0.78

        2       6     3.900        7.3     ‑1.84

        3       5     7.500       13.6      0.82

        4       6    10.000       15.6      1.81

    OVERALL    22                 11.5

H = 5.84  d.f. = 3  p = 0.90

H = 5.85  d.f. = 3  p = 0.90

     

(i) Name: __________________________________

     (ii) Ho: ________________________ ,                                Ha : ____________________

    

    (iii)

Answer 1

(a)  MTB > ttes A c3;    

    SUBC> alte -1.

Test of mu = A vs mu < 0

Variable     N      Mean    StDev   SE Mean         P‑Value

    C3         200    3.8300   0.5403    0.0310         0.90

(i) Name: One sample t-test for mean

(ii) Ho: ,                                          Ha :

iii) conduct the test at a = .05

since p-value = 0.90 > a = .05 so we accept Ho and conclude that .

(b)       MTB > let c3=c2‑c1

     MTB > wtes 0 c3;

     SUBC> alte ‑1.

     TEST OF MEDIAN = 0.000000 VERSUS MEDIAN L.T. 0.000000

                     N FOR   WILCOXON           ESTIMATED

                  N   TEST  STATISTIC  P‑VALUE     MEDIAN

     C3        28     28       82.0 0.003     ‑22.00

(i) Name: Wilcoxon signed rank test

(ii) Ho: Median =0.000  that the median difference between pairs of observations is zero

Ha : Median   that the median difference between pairs of observations not zero

iii) conduct the test at a = .05

since p-value = 0.003 < a = .05 so we reject Ho and conclude that  Median   that the median difference between pairs of observations not zero.

(c) MTB > krusk c5 c6

    LEVEL    NOBS    MEDIAN  AVE. RANK   Z VALUE

        1       5     5.600        9.5     ‑0.78

        2       6     3.900        7.3     ‑1.84

        3       5     7.500       13.6      0.82

        4       6    10.000       15.6      1.81

    OVERALL    22                 11.5

H = 5.84  d.f. = 3  p = 0.90

H = 5.85  d.f. = 3  p = 0.90

     

(i) Name: kruskal wallis test

     (ii) Ho: 5.84 ,

          Ha :5.85

    

iii) conduct the test at a = .05

since p-value = 0.9 > a = .05 so we accept Ho.