Statistics

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.

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  1. 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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