Biostats Questions Midterm 3

Terms in this set (49)

A multimedia program designed to improve dietary behavior among low-income women was evaluated by comparing women who were randomly assigned to intervention and control groups. The intervention was a 30-minute session in a computer kiosk in the Food Stamp office. One of the outcomes was the score on a knowledge test taken about 2 months after the program. Here is a summary of the data:

Group n x s
Intervention 163 5.15 1.15
Control 214 4.33 1.16
(a) The test had six multiple-choice items that were scored as correct or incorrect, so the total score was an integer between 0 and 6. Do you think that these data are Normally distributed? Explain why or why not.
(b) Is it appropriate to use the two-sample t procedures that we studied in this section to analyze these data? Give reasons for your answer.
(c) Describe appropriate null and alternative hypotheses for evaluating the intervention.
Some people would prefer a two-sided alternative in this situation while others would use a one-sided significance test. Give reasons for each point of view.
(d) Carry out the significance test using a one-sided alternative. Report the test statistic with the degrees of freedom and the P-value. (Round your test statistic to three decimal places, your degrees of freedom to the nearest whole number, and your P-value to four decimal places.)
Write a short summary of your conclusion.
(e) Find a 95% confidence interval for the difference between the two means. Compare the information given by the interval with the information given by the significance test. (Round your answer to two decimal places.)
(f) The women in this study were all residents of Durham, North Carolina. To what extent do you think the results can be generalized to other populations?
Dual-energy X-ray absorptiometry (DXA) is a technique for measuring bone health. One of the most common measures is total body bone mineral content (TBBMC). A highly skilled operator is required to take the measurements. Recently, a new DXA machine was purchased by a research lab and two operators were trained to take the measurements. TBBMC for eight subjects was measured by both operators. The units are grams (g). A comparison of the means for the two operators provides a check on the training they received and allows us to determine if one of the operators is producing measurements that are consistently higher than the other. Here are the data:
Subject
Operator 1 2 3 4 5 6 7 8
1 1.326 1.342 1.074 1.225 0.938 1.006 1.182 1.287
2 1.323 1.322 1.073 1.233 0.934 1.019 1.184 1.304
(a) Take the difference between the TBBMC recorded for Operator 1 and the TBBMC for Operator 2. (Operator 1 minus Operator 2. Round your answers to four decimal places.)
Describe the distribution of these differences using words.
(b) Use a significance test to examine the null hypothesis that the two operators have the same mean. Give the test statistic. (Round your answer to three decimal places.)
Give your conclusion.
(c) The sample here is rather small, so we may not have much power to detect differences of interest. Use a 95% confidence interval to provide a range of differences that are compatible with these data. (Round your answers to four decimal places.)
(d) The eight subjects used for this comparison were not a random sample. In fact, they were friends of the researchers whose ages and weights were similar to the types of people who would be measured with this DXA. Comment on the appropriateness of this procedure for selecting a sample, and discuss any consequences regarding the interpretation of the significance testing and confidence interval results.
The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures students' study habits and attitudes toward school. The survey yields several scores, one of which measures student attitudes toward studying. The mean student attitude score for college students is about 60, and standard deviation is about 13. A researcher in the Philippines is concerned about the declining performance of college graduates on professional licensure and board exams. She suspects that poor attitudes of students are partly responsible for the decline and that the mean for college seniors who plan to take professional licensure or board exams is less than 60. She gives the SSHA to an SRS of 169 college seniors in the Philippines who plan to take professional licensure or board exams. Suppose we know that the student attitude scores in the population of such students are Normally distributed with standard deviation σ = 13.
(a) We seek evidence against the claim that μ = 60. What is the sampling distribution of the mean score x of a sample of 169 students if the claim is true?
Draw the density curve of this distribution. (Sketch a Normal curve, then mark on the axis the values of the mean and one, two, and three standard deviations of the sampling distribution on either side of the mean.)
(b) Suppose that the sample data give x = 59.2. Mark this point on the axis of your sketch. In fact, the result was x = 57.2. Mark this point on your sketch. Using your sketch, explain in simple language why one result is good evidence that the mean score of all college seniors in the Philippines who plan to take professional licensure or board exams is less than 60 and why the other outcome is not.
The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures students' study habits and attitude toward school. The survey yields several scores, one of which measures student attitudes toward studying. The mean student attitude score for college students is about 50, and the standard deviation is about 15. A researcher in the Philippines is concerned about the declining performance of college graduates on professional licensure and board exams. She suspects that poor attitudes of students are partly responsible for the decline and that the mean for college seniors who plan to take professional licensure or board exams is less than 50. She gives the SSHA to an SRS of 225 college seniors in the Philippines who plan to take professional licensure or board exams. Suppose we know that the student attitude scores in the population of such students are Normally distributed with standard deviation
σ = 15.
(Use a left-tailed test.)
(a) One sample of 225 students had mean student attitude score
x = 49.6.
Enter this x, along with the other required information, into the P-Value of a Test of Significance Applet. What is the P-value? (Round your answer to four decimal places.)
Is this outcome statistically significant at the
α = 0.05
level? At the
α = 0.01
level?
(b) Another sample of 225 students had
x = 47.6.
Use the applet to find the P-value for this outcome. (Round your answer to four decimal places.)
Is it statistically significant at the
α = 0.05
level? At the
α = 0.01
level?
(c) Explain briefly why these P-values tell us that one outcome is strong evidence against the null hypothesis and that the other outcome is not.
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