A manufacturer of cigarettes wishes to test the claim that

Harken43

Harken43

Answered question

2022-03-03

A manufacturer of cigarettes wishes to test the claim that the variance of the nicotine content of the cigarettes the company manufactures is equal to 0.638 milligram. The variance of a random sample of 25 cigarettes is 0.930 milligram. At α=0.05, test the claim.

Answer & Explanation

Mikayla Swan

Mikayla Swan

Beginner2022-03-04Added 9 answers

Given,
n=25
s2=0.930
α=0.05
The degrees of freedom is obtained as-
df=n-1
=25-1
=24
The hypothesis to be tested here is-
H0:σ2=0.638(claim)
H1:σ20.638
This is a two-tailed test.
The chi-square test statistics is obtained as-
χ2=(n1)s2σ2
=(251)×(0.930)20.638
=34.984
As per chi-squares distribution table, the critical value of the chi-square test statistics for 24 degrees of freedom at 0.05 level of significance is obtained as 36.415
Decision rule: Reject H0: if chi-square test statistics>36.415
Conclusion: Since Chi-square test statistics (34.984) <36.415, therefore there is no evidence to reject the null hypothesis and it can be concluded that there is evidence to support the claim that the variance of the nicotine content of the cigarettes the company manufactures is equals to 0.638 milligram.

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