Fentanyl is often found in illegal drugs and can have lethal effects on a person once injected. A pharmaceutical company has come out with test strips that can detect fentanyl in drugs. They claim that you can test as many as 40 samples of drugs with each strip. You work for the FDA and are concerned that the actual number of drugs is different from this value. You take a sample of 15 test strips and find a mean of 36, with a standard deviation of 6. Test this claim at a significance level of 0.05.

What is the null Hypothesis H0?

What is the alternative hypothesis H₁? What type of alternative hypothesis is this?

What is the test statistic?

What is the critical value?

What is the p-value?

What decision do we make regarding the hypotheses being tested?