1. Professor Williamson is investigating the different types of Iris plants. He has two samples of Irises (50 in each group) that he thinks represent different species. One of the things that would help him to prove this is if the plants are of different dimensions. He decides to look at the sepals and measure their lengths. If he can show that the lengths of the sepals are statistically significantly different he will have some evidence for his hypothesis. He conducts the following T test:

1. What type of T test is this?
2. What assumptions should Professor Williamson have evaluated? Where any of them met?
3. What are the null and the alternate hypotheses (2 tail) for the T test?
4. Interpret the results in terms of the hypotheses in your own words. Does Professor Williamson have evidence that might make him think that he has 2 species of irises?
5. What, in you own words, would happen if Professor Williamson made a type 1 error?

What would be a type II error?

Which of these could have occurred in this case?

1. Dr. Martin is evaluating a new drug to increase hemoglobin levels in anemic patients. He performs an experiment in which he measures hemoglobin levels before and after administration of the drug. The descriptive statistics and a statistical test for an effect of the drug are:

1. What type of T test is this?
2. What assumptions should Dr. Martin have evaluated? Where any of them met?
3. What are the null and the alternate hypotheses (2 tailed) in your own words?
4. Interpret the results in terms of the hypotheses in your own words. Does Dr Martin have reason to be optimistic about the new medication? Note: the data is calculated as pre value – post value.
5. What, in your own words, would happen if Dr. Martin made a type 1 error.
   A type II error?
   Which type of error could have occurred here?
   3. Professor Quagmire tells one of his graduate students that he must "prove" that students in his college ("Own") have higher IQ’s than those in the neighboring college of one of the professor’s archenemies ("Other"). The graduate student manages to get IQ values for 10 students in each college and calculates a T test.
   1. Has he succeeded in meeting the professor’s demand?
      He then goes out and gets 400 IQ’s for each college and calculates a T test.
      b. Has he met the professor’s demand?
      c. What do you think accounts for this difference (from the previous analysis)?
      d. Do you think the IQ difference between the 2 colleges is "practically" significant?
      e. Do you think that "statistically significant" always means "practically significant"?
6. How does this problem relate to the commonly held (at least for statisticians) belief that you can make anything statistically significant if you try hard enough? How could this be done?

1. The following data are taken from a submitted paper: Nierenberg DW, Stukel TA, Karagas MR and the Micronutrient Study Group. The effects of dietary factors and personal characteristics on plasma concentrations of retinol, alpha-tocopherol and five carotenoids. Based on the tables (T test and means) answer the following questions.

1. The T test compares calories consumed per day for males and females. What type of T test is this?
2. What are the assumptions of this T test (what is assumed to be true about the data)?
3. State the null and alternate hypothesis (2 tailed) in terms of the actual measurements.
4. Interpret the results of the T test. Describe what this means about caloric intake?
5. What is the meaning of the 95% confidence interval?

PROBLEMS INCORPORATING SPSS:

The file "calcium.sav" contains results from a randomized comparative experiment that aimed to investigate the effect of calcium on blood pressure in hypertensive men. A treatment group of 10 men received a calcium supplement for 12 weeks, and a control group of 11 men received a placebo during the same period. All subjects had their blood pressure tested before and after the 12-week period.

Variable names in the SPSS file:

1. Group: Whether subject received calcium or placebo
2. Begin: seated systolic blood pressure before treatment
3. End: seated systolic blood pressure after treatment
4. Decrease: Decrease in blood pressure (Begin - End)
   Answer the following questions:
5. Researchers are interested in finding out whether their entire sample suffers from hypertension at study baseline. 140 millimeters of mercury is considered a cut-off point between healthy and unhealthy systolic blood pressure. Researchers need to find out whether the average blood pressure of 21 men is higher than the cut-off point.

1. State the Null hypothesis for this problem.
2. State the Alternative hypothesis for this problem.
3. What statistical test is appropriate to answer the question? Justify your answer.
4. Perform the hypothesis testing in SPSS, providing RELEVANT output.
5. Based on the obtained results in d), do you reject the Null hypothesis? Justify your answer.
6. In plain English, what did you find?

1. Further, researchers are interested in whether blood pressure of 21 men changes from baseline to 3 months follow-up.

1. State the Null hypothesis for this problem.
2. State the Alternative hypothesis for this problem.
3. What statistical test is appropriate to answer the question? Justify your answer.
4. Perform the hypothesis testing in SPSS, providing RELEVANT output.
5. Based on the obtained results in d), do you reject the Null hypothesis? Justify your answer.
6. In plain English, what did you find?

1. Finally, researchers are interested in whether change in blood pressure scores from baseline to 3-month follow-up is associated with calcium intake.
   1. State the Null hypothesis for this problem.
   2. State the alternative hypothesis for this problem.
   3. What statistical test is appropriate to answer the question? Justify your answer.
   4. Perform the hypothesis testing in SPSS, providing RELEVANT output.
   5. Based on the obtained results in d), do you reject the Null hypothesis? Justify your answer.
   6. In plain English, what did you find?

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Solution: The downloadable solution consists of 12 pages, 1834 words and 13 charts.
Deliverable: Word Document