A random sample of 8 cigarettes of a Marlboro has an average nicotine content of 4.2 milligrams and a standard deviation of 1.4 milligrams. Is this I line with the manufacturer's claim that the average nicotine content does not exceed 3.5 milligrams? Use a 0.01 level of significance and assume the distribution of nicotine contents to be normal.
Determine the Critical Region
Answers & Comments
Answer:
0.0793 > 0.01, which means that we have a result in line with the manufacturer's claim.
Step-by-step explanation:
Manufacturer’s claim that the average nicotine content does not exceed 3.5 mg
This means that the null hypothesis is given by:
And the alternate hypothesis is:
The test statistic is:
In which X is the sample mean, is the value tested at the null hypothesis, is the standard deviation and n is the size of the sample.
3.5 is tested at the null hypothesis
This means that
A random sample of 8 cigarettes of a certain brand has an average nicotine content of 4.2 milligrams and a standard deviation of 1.4 milligrams.
This means that
Value of the z-statistic:
Pvalue of the test:
We are testing if the mean is higher than 3.5.
The sample mean found is of 4.2, and we have to find the probability of finding a sample mean at least as large as this, which is 1 subtracted by the pvalue of z = 1.41.
z = 1.41 has a pvalue of 0.9207
1 - 0.9207 = 0.0793
0.0793 > 0.01, which means that we have a result in line with the manufacturer's claim.
Step-by-step explanation:
if im wrong sorry