Posted by **Clay** on Tuesday, November 27, 2012 at 1:49am.

The nicotine content in cigarettes of a certain brand is normally distributed with mean (in milligrams) μ and standard deviation σ = 0.1. The brand advertises that the mean nicotine content of their cigarettes is 1.5, but measurements on a random sample of 400 cigarettes of this brand gave a mean of x =1.52. Is this evidence that the mean nicotine

content is actually higher than advertised? To answer this, test the hypotheses of

H0: μ = 1.5 vs. Ha: μ > 1.5

at a significance level of α = 0.01.

1. The test statistic for this test is

A) z = -4.00

B) z = -0.20

C) z = 0.20

D) z = 4.00

2. Based on the p-value of the test and the given significance level, what would you

conclude?

A) Fail to reject H0, indicating evidence that the mean nicotine content in this brand of

cigarettes equals 1.5 milligrams.

B) Reject H0, indicating evidence that the mean nicotine content in this brand of

cigarettes is greater than 1.5 milligrams.

C) There is a 5% chance that the null hypothesis is true.

D) We cannot make a conclusion here since we do not know the true mean of the

population.

- Statistics -
**PsyDAG**, Tuesday, November 27, 2012 at 12:56pm
Z = (mean1 - mean2)/standard error (SE) of difference between means

SEdiff = √(SEmean1^2 + SEmean2^2)

SEm = SD/√n

If only one SD is provided, you can use just that to determine SEdiff.

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score to answer 2.

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