Assume that a simple random sample has been selected from a normally distributed

Question

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. A simple random sample of 25 filtered 100 mm cigarettes is obtained, and the tar content of each cigarette is measured. The sample has a mean of 19.2 mg and a standard deviation of 3.86 mg. Use a 0.05 significance level to test the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg, which is the mean for unfiltered king size cigarettes. What do the results suggest, if anything, about the effectiveness of the filters?

Explanation / Answer

here null hypothesis" mean >=21.1

alternate hypothesis: mean <21.1

here std error of the mean =std deviation/(n)1/2 =0.772

hence test stat t=(X-mean)/std error =(19.2-21.1)/0.772=-2.4611

for above p value at 24 degree of freedom =0.0107

as p vlaue is less then 0.05 level, we reject null hypothesis, and conclude that filter is effective in reducing tar.

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