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 you believe that the mean nicotine content is actually higher than advertised. To explore this, you test the hypotheses H0:μ=1.5, Ha:μ>1.5 and you obtain a P-value of 0.052. Which of the following is true? A. At the α=0.05 significance level, you have proven that H0 is true. B. This should be viewed as a pilot study and the data suggests that further investigation of the hypotheses will not be fruitful at the α=0.05 significance level. C. There is some evidence against H0, and a study using a larger sample size may be worthwhile. D. You have failed to obtain any evidence for Ha.

Question

Aydin

Mathematics

27 March, 14:30

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 you believe that the mean nicotine content is actually higher than advertised. To explore this, you test the hypotheses H0:μ=1.5, Ha:μ>1.5 and you obtain a P-value of 0.052. Which of the following is true? A. At the α=0.05 significance level, you have proven that H0 is true. B. This should be viewed as a pilot study and the data suggests that further investigation of the hypotheses will not be fruitful at the α=0.05 significance level. C. There is some evidence against H0, and a study using a larger sample size may be worthwhile. D. You have failed to obtain any evidence for Ha.

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Answers (1)

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Jennifer Moran · Answer 1

Step-by-step explanation:

This is a test of a single population mean since we are dealing with mean.

From the information given,

Null hypothesis is expressed as

H0:μ=1.5

The alternative hypothesis is expressed as

Ha:μ>1.5

This is a right tailed test

The decision rule is to reject the null hypothesis if the significance level is greater than the p value and accept the null hypothesis if the significance level is less than the p value.

p value = 0.052

Significance level, α = 0.05

Since α = 0.05 < p = 0.052, the true statement would be

At the α=0.05 significance level, you have proven that H0 is true. B.