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1. Body Mass Index (BMI) is a measure used to determine whether someone is underweight, of normal weight, overweight, or obese. For 60-year old women in the United States, the standard deviation for BMI is 7. From a sample of 81 women, you have calculated a mean of 28 and a standard deviation of 7.2. 

a. What is the point estimate for the population mean? (2)

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b. What is the error bound of the mean (EBM) for the 95% confidence interval? (2)

c. What values mark the 95% confidence interval? (2)  

d. What is the probability that the population mean falls outside of the calculated 95% confidence interval? (2)

PSYC A303: STATISTICS AND METHODS NAME:

EXAM 3 (CLASSES 12-18)

FOR EACH OF THE FOLLOWING QUESTIONS, PLEASE PROVIDE THE INFORMATION THAT IS REQUESTED. THE POINT VALUE OF EACH QUESTION (OR EACH PART) IS INDICATED IN PARENTHESES AT THE END OF THE QUESTION. TOTAL POINT VALUE IS 50. EQUATIONS AND FORMULAS THAT MIGHT BE NEEDED ARE ON THE LAST PAGE OF THIS EXAM. TABLES FOR z, t, and F WILL BE NEEDED – USE AS APPROPRIATE. PLEASE BE SURE TO PROVIDE YOUR CALCULATIONS – SHOW YOUR WORK.

CONFIDENCE INTERVALS

1. Body Mass Index (BMI) is a measure used to determine whether someone is underweight, of normal weight, overweight, or obese. For 60-year old women in the United States, the standard deviation for BMI is 7. From a sample of 81 women, you have calculated a mean of 28 and a standard deviation of 7.2.

a. What is the point estimate for the population mean? (2)

b. What is the error bound of the mean (EBM) for the 95% confidence interval? (2)

c. What values mark the 95% confidence interval? (2)

d. What is the probability that the population mean falls outside of the calculated 95% confidence interval? (2)

2. A pharmaceutical company makes tranquilizers, which are anti-anxiety drugs. The type of drug most commonly used these days are benzodiazepines. It is assumed that the distribution for the length of time they are effective is approximately normal. Researchers in a hospital used the drug on a random sample of nine patients. The effective period of the tranquilizer for each patient (in hours) was as follows: 2.7; 2.8; 3.0; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4, which yields a mean of 2.51 hours and a standard deviation of 0.318. As it is very important to accurately assess drug effects, determine the 99% confidence interval for the population mean, as well answering the associated questions.

a. What is the error bound of the mean (EBM)? (2)

b. What values mark the 99% confidence interval for the population mean? (2)

c. How many degrees of freedom are associated with this analysis? (1)

d. What is the probability of the population mean falling within this confidence interval? (1)

e. What is the probability of the population mean falling outside of this confidence interval? (1)

3. With respect to z-distributions and t-distributions, which of the two distributions has more of the area in the tails of the distribution, and thus, less in the “body” of the distribution? (1)

HYPOTHESIS TESTING

4. Describe each of the following in terms of accepting, not accepting, rejecting, and/or not accepting hypotheses.

a. Type I error. (2)

b. Type II error. (2)

Not rejecting null hypothesis while in fact there is some differences between the groups

5. Which one of the following statements is one that should not be said (or written)? Can highlight or bold your answer, or put into a clearly different color font. (1)

a. The null hypothesis could not be rejected.

b. The alternative hypothesis was accepted

c. The null hypothesis was accepted.

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