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