Question

(a)Jordan Almonds have a colored candy coating with colors: Yellow, Green, Purple, Pink, White, and Blue. In a single bag the frequencies were 18, 24, 26, 17, 16, 28, resp. Are the frequencies consistent with an equal distribution of colors?   

(b)A second bag had frequencies 17, 26, 15, 14, 16, and 22, resp. Is this bag also consistent with equal distribution of colors? A third bag had frequencies 11, 27, 17, 22, 19, and 21, resp. Can the bags be pooled?

Answer 1

I used MINITAB software to solve this question.

Go through following steps to get answer.

Step.1 Enter data in minitab.

Step.2 Go to 'Stat' ----> 'Tables' ----> 'Chi-square test of Goodness-of-fit'.

Step.3 New window pop-up on sceen. Refer follwing screen shot and enter information accordingly.

Step.4 Repeat above steps for sample 2 and 3

Hypothesis:

H0 : All colours have equal probabilities

H1 : Probabilities of all colours are not same.

Minitab output:

Chi-Square Goodness-of-Fit Test for Observed Counts in Variable: Sample 1

Test Contribution
Category Observed Proportion Expected to Chi-Sq
1 18 0.166667 21.5 0.56977
2 24 0.166667 21.5 0.29070
3 26 0.166667 21.5 0.94186
4 17 0.166667 21.5 0.94186
5 16 0.166667 21.5 1.40698
6 28 0.166667 21.5 1.96512

N DF Chi-Sq P-Value
129 5 6.11628 0.295

Chi-Square Goodness-of-Fit Test for Observed Counts in Variable: Sample 2

Test Contribution
Category Observed Proportion Expected to Chi-Sq
1 17 0.166667 18.3333 0.09697
2 26 0.166667 18.3333 3.20606
3 15 0.166667 18.3333 0.60606
4 14 0.166667 18.3333 1.02424
5 16 0.166667 18.3333 0.29697
6 22 0.166667 18.3333 0.73333

N DF Chi-Sq P-Value
110 5 5.96364 0.310

Chi-Square Goodness-of-Fit Test for Observed Counts in Variable: Sample 3

Test Contribution
Category Observed Proportion Expected to Chi-Sq
1 11 0.166667 19.5 3.70513
2 27 0.166667 19.5 2.88462
3 17 0.166667 19.5 0.32051
4 22 0.166667 19.5 0.32051
5 19 0.166667 19.5 0.01282
6 21 0.166667 19.5 0.11538

N DF Chi-Sq P-Value
117 5 7.35897 0.195

Since p-values for all three samples are greater than 0.05, hence we accept null hypothesis at 5% level of significance. And conclude that frequencies consistent with an equal distribution of colors.

Since all bags having approximately equal proportion of each color, hence we can pool bags.