Question

The quality of four brands of orange juice (OJ) are assessed by independent groups
of judges, five in each group, who assign scores to them.

Summary measures are obtained using SPSS :
a) Is there reason to believe that all samples are drawn from normal
populations ? Discuss. (No calculation is needed here)
b) Test whether there is a difference in the mean scores.
OJ-1 OJ-2 OJ-3 OJ-4
8 7 6 5
8 8 6 5
9 5 7 9
9 10 7 6
7 8 12 11
OJ Mean N Variance
1 8.20 5 0.700
2 7.60 5 3.300
3 7.60 5 6.300
4 7.20 5 7.200
Total 7.65 20 3.818
Kolmogorov-Smirnov Shapiro-Wilk
Statistic df Sig. Statistic df Sig.
OJ-1 .231 5 .200 .881 5 .314
OJ-2 .213 5 .200 .963 5 .826
OJ-3 .394 5 .011 .710 5 .012
OJ-4 .273 5 .200 .852 5 .201

Answer 1

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a) No we can't believe it because sample size of each sample is 5 which is very small. If we have a sample size atleast 30 then we can apply Central Limit Theorem.

b) at significance level 0.05 we have OJ -1 , OJ -2 and OJ -4 have p value greater than 0.05 for both test. So these three samples hold Normality assumption. But OJ - 3 doesn't hold it since p value is less than 0.05 for both test.