# Statistics

posted by .

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 -

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.

## Similar Questions

1. ### Statistics

Im kind of confused on this question?? To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine found in all commercial brands of cigarettes. A new cigarette recently
2. ### Stastics

To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine found in all commercial brands of cigarettes. A new cigarette has recently been marketed. The FDA tests on …
3. ### Statistics

To determine whether themean nicotine content of a brand of cigarettes is greater than the advertised value of 1.4 milligrams, a health advocacy program tests: Ho: mu = 1.4 Ha: mu > 1.4 The calculated value of the test statistic …
4. ### statistics

For each of the following questions, decide whether or not the sample data can be used to construct a confidence interval. How do I go about determining if the sample data can be used to construct a confidence interval?
5. ### Statistics

Cigarette companies advertise that the mean amount of nicotine in each cigarette is 1.4 milligrams. A health advocacy group believes that the amount of nicotine is greater than the advertised amount. They hire a consultant who collects …
6. ### statistics

A tobacco company claims that the nicotine content of its "light" cigarettes has a mean of milligrams and a standard deviation of milligrams. What is the probability that randomly selected light cigarettes from this company will have …
7. ### statistics

A tobacco company claims that the nicotine content of its "light" cigarettes has a mean of milligrams and a standard deviation of milligrams. What is the probability that randomly selected light cigarettes from this company will have …
8. ### statistics

How large a sample would be needed to form a 90% confidence interval for the mean nicotine content of a brand of cigarettes if the nicotine content has a normal distribution with sigma equal to 8.5 mg and the width of the interval …
9. ### Probability & Statistics

To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine found in all commercial brands of cigarettes. A new cigarette has recently been marketed. The FDA tests on …
10. ### Statistics

A tobacco company claims that the nicotine content of its "light" cigarettes has a mean of milligrams and a standard deviation of milligrams. What is the probability that randomly selected light cigarettes from this company will have …

More Similar Questions