All questions below are based on the following: Generic drugs are lower-cost substitutes for brand-name drugs

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All questions below are based on the following:

Generic drugs are lower-cost substitutes for brand-name drugs. Before a generic drug can be sold in the US, it must be tested and found to perform equivalently to the brand-name product. The US Food and Drug Administration is now supervising the testing of a new generic antifungal ointment. The brand-name ointment is known to deliver a mean of 3.5 micrograms of active ingredient to each square centimeter of skin.

 

As part of the testing, seven subjects apply the ointment. Six hour later, the amount of drug that has been absorbed into the skin in measured. The amounts, in micrograms, are

 

                     2.6, 3.2, 2.1, 3.0, 3.1, 2.9, 3.7

 

How strong is the evidence that the mean amount absorbed differs from 3.5 micrograms? Use α=0.01. Assume that the population is approximately normal.

 

1. We need to check it the assumptions for the methods introduced in this are satisfied. The sample size that is in our case equal to _____________ it is less than 30. In this case, in order to apply the methods, we need to know that the population is approximately ____________
2.  Which of the following are the correct hypotheses? Null hypothesis is , Alternative hypothesis is
3. In the study population standard deviation is (known or unknown)
4.  To test this hypothesis we will use _____________ distribution
5. Calculate standard deviation of the sample. Round it to the nearest hundredth.
6. Calculate the test statistic. Round the result to the nearest hundredths.
7. Using the following site: P-value calculator (Links to an external site.) find the p-value (use the value of the test statistic that is rounded to the nearest hundredth). Do not round the p-value. 
8. To determine if we reject or fail to reject the null hypothesis we need to compare the p-value with the following number (you answer should be a number not a word):
9. In our case, P-value is the probability of obtaining test results.  under the assumption that
10. Because the p-value is _____________ than the chosen level of significance, we_____________ null hypothesis
11. We conclude that (there is or there is not) enough evidence to conclude that the mean amount of drug absorbed differs from 3.5 micrograms.
12. Suppose that instead of using α=0.01 we choose α=0.05. In this case we would (reject or fail to reject) the null hypothesis. In such case we would conclude that (there is or there is not) enough evidence to support the claim that the mean amount of drug absorbed differs from 3.5 micrograms.