Smarties (sugar coated chocolate confectionary) come in 8 colours -green, yellow

Question

Smarties (sugar coated chocolate confectionary) come in 8 colours -green, yellow, red, orange, pink, purple, blue and brown. You buy a bag containing 120 smarties to investigate the distribution of colours, and count 12 green, 14 yellow, 17 red, 15 orange, 16 pink, 17 purple, 11 blue and 18 brown smarties. a) If Smarties are packaged in equal proportions, how many of each colour would you expect in the bag? b) To see if your results are unusual, will you perform a goodness-of-fit test or a test of independence? c) State your hypotheses. d) Check the conditions. e) How many degrees of freedom are there? f) Find chi^2 and the P-value. g) State your conclusion.

Explanation / Answer

a)as there are 8 colors in equal proportion; hence expected count of each color =120/8=15

b) we will apply chi square goodness of fit to test if all color count are in equal proportion

c) null hypothesis: each color is in equal proportion distributed.

alternate hypothesis:at least one color is not in equal proportion distributed.

d) as expected value in each cell is greater then 5 we can apply chi square test

e)degree of freedom =k-1=8-1=7

f)

for above test chi square X2 =2.9333

and p value=0.8911

g) as p value is significantly high; we can not reject null hypothesis that colors are equally distributed

observed Expected Chi square X Probability O E=total*p =(O-E)^2/E green 1/8 12.000 15.00 0.60 yellow 1/8 14.000 15.00 0.07 red 1/8 17.000 15.00 0.27 orange 1/8 15.000 15.00 0.00 pink 1/8 16.000 15.00 0.07 purple 1/8 17.000 15.00 0.27 blue brown 1/8 11.000 15.00 1.07 65-75 1/8 18.000 15.00 0.60 1 120 120 2.9333

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