16.5 - Using Minitab to Lighten the Workload

This is how I used Minitab to help with the calculations of the alpha particle example on the Unspecified Probabilities page in this lesson.

1. Use Minitab's Calc >> Probability distribution >> Poisson command to determine the Poisson(5.6) probabilities:

   Poisson with mean = 5.6

   x	P (X = x)
   0	0.003698
   1	0.020708
   2	0.057983
   3	0.108234
   4	0.151528
   5	0.169711
   6	0.158397
   7	0.126717
   8	0.088702
   9	0.055193
   10	0.030908
   11	0.015735
   12	0.007343

   1. Enter the observed counts into one column and copy the probabilities (collapsing some categories, if necessary) into another column. Use Minitab's Calc >> Calculator command to generate the remaining necessary columns:

      Poisson with mean = 5.6

      Row	Obsd	p_i	Expd	Chisq
      1	5	0.082389	8.2389	1.27329
      2	15	0.108234	10.8234	0.43772
      3	19	0.151528	15.1528	0.97678
      4	16	0.169711	16.9711	0.05557
      5	15	0.158397	15.8397	0.04451
      6	9	0.126717	12.6717	1.06390
      7	12	0.088702	8.8702	1.10433
      8	7	0.055193	5.5193	0.39724
      9	4	0.053986	5.3986	0.36233

      Sum up the "Chisq" column to obtain the chi-square statistic Q.

2. 

This is how I used Minitab to help with the calculations of the IQ example on the Continuous Random Variables page in this lesson.

1. The sorted data:

   Sample

   54	66	74	74	75	78	79	80	81	82
   82	82	83	84	87	88	88	88	88	89
   89	89	89	89	90	90	90	91	92	93
   93	93	94	96	96	97	97	98	98	99
   99	99	99	99	100	100	100	102	102	102
   102	102	103	103	104	104	104	105	105	105
   105	106	106	106	107	107	108	108	108	109
   109	109	110	111	111	111	111	112	112	112
   114	114	115	115	115	116	118	118	120	121
   121	122	123	125	126	127	127	131	132	139

   1. The working table:

      Row	CProb	Z	Sample	Obsd	Expd	Chisq
      1	0.1	-1.28155	79.495	7	10	0.9
      2	0.2	-0.84162	86.534	7	10	0.9
      3	0.3	-0.52440	91.610	14	10	1.6
      4	0.4	-0.25355	95.946	5	10	2.5
      5	0.5	0.00000	100.000	14	10	1.6
      6	0.6	0.25355	104.054	10	10	0.0
      7	0.7	0.52440	108.390	12	10	0.4
      8	0.8	0.84162	113.466	11	10	0.1
      9	0.9	1.28155	120.505	9	10	0.1
      10				11	10	0.1

2. The chi-square statistic: