1. A medical researcher wants to test the effectiveness of the new cholesterol drug by comparing it to the existing most common drug.

To test the claim, a sample of 40 patients with high cholesterol is chosen at random from a cardiologist's list of patients to take the new drug. Over the course of three months, this group lowers its total cholesterol by a mean of 45.7 points. The population standard deviation for this group is known to be 5.8 points. Another 60 patients with high cholesterol are chosen at random from a cardiologist's list of patients and are asked to continue taking the old drug. This group lowers its total cholesterol level by a mean of 34.6 points. The population standard deviation for this group is known to be 5.9 points. With 1% level of significance, test the claim that the average decrease of cholesterol level from using the new drug is different from average decrease of cholesterol level from using the old drug.

a. Assumptions: (select everything that applies from below)

• Paired samples
• Population standard deviation are unknown
• Population standard deviation are unknown but assumed equal
• Simple random samples
• Independent samples
• The number of positive and negative responses are both greater than 10 for both samples
• Population standard deviations are known
• Normal populations
• Sample sizes are both greater than 30

2. A group of researchers wants to compare the men's life expectancy to women's life expectancy in the US in 2018. Historically, the population standard deviation of men's life expectancy is known to be 15.7 years and of women's life expectancy is 13.3 years. The average life expectancy among 40 men in the sample was found to be 77.6 years and the average life expectancy among 60 women in the sample was found to be 82.8 years. At 5% significance level, test the claim that men's life expectancy different from life expectancy of women in the US in 2018.

a. Assumptions: (select everything that applies from below)

• Population standard deviation are unknown but assumed equal
• Population standard deviations are known
• Paired samples
• Simple random samples
• Population standard deviation are unknown
• Independent samples
• The number of positive and negative responses are both greater than 10 for both samples
• Normal populations
• Sample sizes are both greater than 30

3. A researcher takes a random sample of 15 ten-year-old girls and a separate random sample of 20 ten-year-old boys in the United States. The results are shown below:

Girls:

58.7	56.5	55.2	57.2	51.8
53	57.8	53.6	52.8	54.4
51.5	51.3	58.2	59.2	53.6

Boys:

55.8	56.6	54.2	56.5	64
55.7	53.9	59.9	52.3	58.2
59.4	60.6	65.1	62.9	57.6
57.7	54.4	51.1	55	52.8

After analyzing the data, the researcher reports that the mean height of the girls and the standard deviation are 55 inches and 2.75 inches respectively and the mean height of the boys and the standard deviation are 57.2 inches and 3.87 inches respectively. Based on information from the U.S. National Health and Nutrition Examination Survey (NHANES), the heights of ten-year-old girls follow a normal distribution with population standard deviation 2.9 inches and the heights of ten-year-old boys follow a normal distribution with population standard deviation 3.9 inches. Test at a 10% level of significance whether the data indicate that the average height of ten-year-old girls is the same as the average height of ten-year-old boys.

What are the correct hypotheses?

a. H₀: Select an answer p 1 x 1 s 1 1 p 1 1 1 s 1 > = <

Select an answer 2 s 2 2 2 x 2 p 2 s 2 p 2

b. H_A: Select an answer s 1 1 1 s 1 p 1 p 1 x 1 1 < > =

Select an answer s 2 p 2 2 2 p 2 s 2 2 x 2

Based on the hypotheses, find the following:

c. Test Statistic z = d. p-value =

e. Based on the above we choose to Select an answer: Accept the null hypothesis, Accept the alternative hypotheis, Fail to reject the null hypothesis, Reject the null hypothesis.

f. The correct summary would be: Select an answer :There is not enough evidence to reject the claim, There is enough evidence to reject the claim, There is enough evidence to support the claim, There is not enough evidence to support the claim,______ that the average height of ten-year-old girls is the same as the average height of ten-year-old boys.