10. A sample of cereal boxes is randomly selected and the sugar contents (grams

Question

10. A sample of cereal boxes is randomly selected and the sugar contents (grams of sugar per gram of cereal, which are known to be normally distributed) are recorded. Those amounts are summarized with these statistics: n-34, 0.36 g, s-0.18 g. Use a 0.05 significance level to test the claim of a cereal lobbyist that the mean for all cereals is less than 0.31 g. State the . hypothesis name of the appropriate test and if normality is needed, . test statistic value, . pvalue, and . final conclusion.

Explanation / Answer

Sol:

hypothesis

Null hypothesis:

Ho:mu=0.31

Alternative hypothesis

H1:mu<0.31

ALPHA=0.05

name of test:

t test for mean

as n=34 n>30

accorinding to central limit theorem.

normality assumption is satisfied.

Test statistic value

t=samplemean-pop mean/samplesd/sqrt(n)

=0.36-0.31/0.18/sqrt(34)

=1.619

p value is

df=n-1=34-1=33

alpha=0.05

alpha/2=0.05/2=0.025

p=0.057483

final conclusion is

as p>alpha

Fail to reject Null Hypothesis

Accept Null Hypothesis

There is no sufficient evidence at 5% level of significance to support the claim that the mean for all cereals is less than 0.31g.

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