1. Suppose a researcher is interested in investigating the effectiveness of a new diet plan at reducing BMI among a group of women with similar baseline weights after 1 year. Suppose the group of 45 women vary approximately according to a normal distribution with mean BMI (kg/m2) of 29.5 and a standard deviation of 1.6 kg/m2 after 1 year and the goal BMI was 28.5 kg/m2.

A) Did the women meet their goal weight? Use an alpha level of 0.05.
B) State your null and alternative hypotheses, and interpret your pvalue.

2. Suppose a researcher is interested in a new treatment plan for increasing CD4 cell count in immune-compromised patients with HIV. In order to investigate the new drug, the researcher gathers a group of 48 individuals with a mean CD4 count of 317 cells/mm3 after treatment with a standard deviation of 24.6. Test the hypothesis that the mean CD4 count has increased above the goal of 275 cells/mm3. Write out your hypotheses and correctly interpret your pvalue. (Use an alpha level of 0.01)

3. Suppose a researcher is planning a step-by-step smoking cessation program aimed at youth aged 16-18 years old that have been smoking for over a year. After 1 month, the program is intended to get people down below 1 pack of cigarettes (20 cigarettes) a week. Suppose after 1 month, a group of 62 smokers in this age range are smoking an average of 11.6 cigarettes a week with a standard deviation of 2.7. Is there sufficient evidence that the cessation program is working? Set up your hypotheses and interpret your pvalue correctly using the alpha level of 0.05.

4. Suppose a researcher tested the hypothesis that a new anti-hypertensive drug can lower systolic blood pressure in high cholesterol patients below 135 mm HG, and rejected the null hypothesis with a set confidence level of 95%. The researcher had a SRS of 56 patients. Suppose the standard deviation was 19. What is the power of that test of significance aimed at identifying a population with a systolic blood pressure of 110 mm HG?

5. A researcher is interested in investigating the power of his statistical test analyzing the success rate of increasing forced vital capacity (FVC) in children with asthma. Suppose the researcher conducted a z test for significance with a SRS of 74 on a population with a mean FVC of 84% with a null hypothesis that mean FVC was equal to 76%. The prior research determined the standard deviation was 1.2%. What was the power of the test at 95% confidence?

6. How many participants are needed to be enrolled in a study looking at early onset of dementia in a population of middle-aged adults with a power of 90%? Assuming the population as a standard deviation of 7 years, and the detectable difference of interest in age is 6 years, perform the sample size calculation at 95% confidence.

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