2. The Carolina Tobacco Company advertised that its best-selling nonfiltered cig

Question

2. The Carolina Tobacco Company advertised that its best-selling nonfiltered cigarettes contain at most 40 mg of nicotine, but Consumer Advocate magazine ran tests of 10 randomly selected cigarettes and found the amounts (in mg) shown in the list below. It’s a serious matter to charge that the company advertising is wrong, so the magazine editor chooses a significance level of = 0.01 in testing her belief that the mean nicotine content is greater than 40 mg. Using a 0.01 significance level, test the editor’s belief that the mean is greater than 40 mg.

47.3 39.3 40.3 38.3 46.3 43.3 42.3 49.3 40.3 46.3

Show all the steps of your hypothesis test including a) the claim being tested , b) the null and alternative hypothesis, c) the test statistic, d) the p value, e) initial conclusion, and f) a final conclusion about the original claim.

Explanation / Answer

Set Up Hypothesis
Null, H0: U=40
Alternate, mean nicotine content is greater than 40 mgH1: U>40
Test Statistic
Population Mean(U)=40
Sample X(Mean)=43.3
Standard Deviation(S.D)=3.8006
Number (n)=10
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =43.3-40/(3.8006/Sqrt(10))
to =2.746
| to | =2.746
Critical Value
The Value of |t | with n-1 = 9 d.f is 2.821
We got |to| =2.746 & | t | =2.821
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Right Tail - Ha : ( P > 2.7458 ) = 0.01132
Hence Value of P0.01 < 0.01132,Here We Do not Reject Ho

We do n't have evidence that mean nicotine content is greater than 40 mg

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