Course: Statistics and data Analysis

Part 1A

There are no numbers involved in this problem! It is all about demonstrating your understanding of the concepts.

You have been hired by a company that manufactures homeopathic remedies as a data analyst. In particular, they wish to publish a study purporting to show that "allium cepa" is helpful for treating symptoms of the common cold. They ask you to set up a hypothesis test to test the powers of this compound. Using the steps discussed in lecture, describe how you would set up this test.

1. Describe your null hypothesis, alternative hypothesis. Hint: When deciding which is Ho and Ha, remember that the company is hoping to prove that the drug works.

2. Then state what very simple experiment you might do to evaluate allium cepa.

Note: This part does NOT have to be long -- in fact it can should just be a relatively short paragraph. ) That is, do not bother going into specific numbers or stratification. Just explain the two basic groups you would use. You can assume that the control group woud be a placebo.

3. The company asks you to use a significance level of 0.25 in your conclusions. Explain how using this level instead of the standard level of 0.05 might affect the conclusions drawn from your hypothesis test. That is, why might the company ask you to use a significance level of 0.25?

Part 1B

An agricultural company has manufactured a soil compound that they believe will help wheat crops grow faster than the current "leading brand". Over a 3-week period, the leading brand grows an average of 32 inches. The company tests 40 samples of their compound and finds a growth of 34.5 inches, with a standard error (s) of 6.6. Complete a hypothesis test to determne whether the company can claim that their new compound has greater growth than the leading brand's growth. In addition to your numerical answer, be sure to write out the steps of the hypothesis testing process as discussed in lecture.

For purposes of this problem, for your comparison, do not focus on greater or less than. Instead, simply determine if the company's new compound has a different growth rate than the leading brand. In other words, use a 2-tailed test. (Using 2-tailed tests is quite common in scientific testing -- even when the original question is purporting to establish that some new value is "more" or "less" than some original value.)

Hint: Remember that if you end up with a positive test statistic, you want to determine the area under the curve to the RIGHT of the z-statistic (not the left).

Your answer should be done in the traditional ("older") hypothesis test format. That is, do not use the confidence interval method for this question. You will use the (preferred) confidence interval method in a problem below.

Remember that, as has been discussed repeatedly, at the end of the day, the analyst must be able to describe their statistical calculations in "real world" language to assist non-experts in making their decisions. Complete your analysis by answering the following in non-statistical terms: Do the results of the hypothesis test support the company's belief that their soil compound does indeed have a different growth rate from the "leading brand"?

Part 1C

A pharmaceutical company wants to determine whether a new blood pressure medication, Depaulodipine they have developed is more effective than a medication developed by one of their competitors. In particular, their medication is intended to lower the systolic blood pressure of people with moderate hypertension (i.e. moderately elevated systolic blood pressure). Mild (systolic) hypertension is typically defined as a pressure between 140 and 160.

To test the efficacy of their drug, the manufacture took a group of 40 individuals with moderate hypertension, and gave them a course of Depaulodipine. Here are the pressures after their course of treatment:

123, 130, 134, 118, 131, 131, 126, 126, 126, 125, 127, 124, 125, 129, 134, 128, 127, 125, 125, 140, 130, 127, 127, 131, 126, 122, 132, 124, 129, 125, 134, 127, 126, 127, 121, 123, 119, 123, 128, 127

In other words at the end of the treatment, one person had a blood pressure of 123, another had a blood pressure of 130, etc.

Your mean value should be 127.

By comparison, after treatment with the competitor's drug, the systolic blood pressure of all the people in that group (i.e. the control group) had a mean value of 129.

Using the confidence interval technique of hypothesis testing for your calculations, report whether the company can claim that Depaulodipine does a better job of reducing blood pressure than the competitor's drug. Use the standard value for C.