1) A pharmaceutical company is testing a new cold medicine to determine if the drug has side effects

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1) A pharmaceutical company is testing a new cold medicine to determine if the drug has side effects. To test the drug, 7 patients are given the drug and 8 patients are given a placebo (sugar pill). The change in pulse rate (beats per minute) after taking the pill was as follows:

Given drug:

3

7

2

8

2

5

6

Given placebo:

2

4

1

1

2

0

2

3

Test to determine if the drug raises patients' pulse rate more than the placebo using α = 0.025

2.      Corn plants grow to a mean height of 6.43 feet with a standard deviation of 0.15 feet and the distribution of heights is approximately normal. A new genetically modified corn plant is being developed. A researcher grew a group of 27 genetically modified corn plants and found that their mean height was 6.51 feet. Test to determine if the genetically modified plants are taller using α = 0.01.

3.      A recent poll of 2,800 US adults found that 1862 of them had voted in the recent election. Make a 95% confidence interval for the percent of all US adults who voted. (Hope you were one of them, if you are eligible!!)

4.        From the population of all Americans with high cholesterol, which has a mean cholesterol level of 265 mg/dL with a standard deviation of 37, Isis Pharmaceuticals chose 39 patients for treatment with its new antisense drug. After treatment, the patients in the study had a mean cholesterol level of 252. Test to determine if the antisense drug lowered the cholesterol using α = 0.01 and the prob-value approach.

5. The IRS claims that it takes 87 minutes to prepare a tax form. You believe it takes longer than 87 minutes. You ask 21 tax filers and find the following preparation times:

64, 69, 75, 75, 87, 89, 94, 96, 97, 98, 98, 99, 100, 100, 105, 108, 110, 112, 119, 122, 128

Determine if the preparation time is significantly longer than 87 minutes. Use α = .05.

6. Given below are the birth weights of babies born to mothers who took special vitamin supplements while pregnant: 

3.51   4.59   3.93   4.33   3.39   3.68   4.68   3.52    3.84

3.12   4.29   2.27   4.13   4.47   3.20   3.48   2.67     3.40

a. Make a 95% confidence interval for the mean weight of babies whose mothers take vitamin supplements.

b. Do a hypothesis test to determine if these babies' weights are  more than the mean weight for the population of all babies which is 3.41 kg using α = .025

c. In a short paragraph, describe the relationship between your answer to part (a) and your answer to part (b).

7.  A student wanted to study the ages of couples applying for marriage licenses in his county. He studied a sample of 94 marriage licenses and found that in 63 cases the husband was older than the wife. Do the sample data provide evidence that the husband is usually older than the wife among couples applying for marriage licenses in that county? Explain briefly and justify your answer using the methods studied in this course. Use α= 0.05 as the level of significance