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 this cigarette gave a mean nicotine content of 26.8 milligrams and standard deviation of 2.7 milligrams for a sample of nequals9 cigarettes. The FDA claims that the mean nicotine content exceeds 29.9 milligrams for this brand of cigarette, and their stated reliability is 95%. Do you agree?

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and is not enough evidence to conclude that the claim is true.

Step-by-step explanation:

Data given

represent the sample mean

represent the sample standard deviation

sample size  

represent the value that we want to test

represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

represent the p value for the test (variable of interest)  

System of hypothesis

We need to conduct a hypothesis in order to check if the true mean exceed 29.9 or no, the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

The statistic is given by:

 (1)  

Calculate the statistic

We can replace in formula (1) the info given like this:  

P-value

The degrees of freedom are given by:  

Since is a one sided test the p value would be:  

Conclusion  

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and is not enough evidence to conclude that the claim is true.

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