A tobacco company claims that its best-selling cigarettes contain at most 40 mg of nicotine.

Question

This claim is tested at the 1% significance level by using the results of 15 randomly selected cigarettes. The mean is 42.6 mg and the standard deviation is 3.7 mg. Evidence suggests that nicotine is normally distributed. Information from a computer output of the hypothesis test is listed.

Sample mean = 42.6

P − value = 0.008

Sample standard deviation = 3.7

Significance Level = 0.01

Sample Size = 15

Test statistic t = 2.72155

Degrees of freedom = 14

Critical value t = 2.62610

1. Is this a z test or a t-test?

2. Is this a right-tailed, left-tailed, or two-tailed test?

3. From observing the P-value, what would you conclude?

4. By comparing the test statistic to the critical value, what would you conclude?

5. What has been proven in this study?

Answer 1

Since the t-stat is used it is obviously a t test

Since the claim includes the words "at most" , then the null hypothesis is:

Ho: mean <= 40

Ha: mean > 40

a right tailed test

We can reject the null hypothesis based on the p-value < level of significance and t-stat > critical value

There is statistical evidence that the cigarettes contain more than 40 mg of nicotine at the 0.01 significance level.