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A researcher wishes to determine if vitamin E supplements could increase cognitive ability among elderly women. In 2021 the researcher recruited a sample of elderly women aged 50-65. At the time of the enrolment into the study, the women were randomised to either take Vitamin E, or a placebo for six months. At the end of the six-month period, the women were given a cognition test. Higher scores on this test indicate better cognition. The mean and standard deviation of the test scores of 400 women who took vitamin E supplements was 20 and 5 respectively. The mean and standard deviation of the test scores of the 500 women who took placebo supplements was 25 and 2, respectively.   REQUIRED: Construct a 99% confidence interval for the mean difference in cognition test scores between Vitamin E and placebo groups. Interpret your answer.         Describe the effect on the confidence interval in (a) women who took vitamin E supplements increased to 600 and those who took placebo supplements increased to 750 women assuming other measurements remained constant.             What are the limitations to this study for drawing conclusions about whether or not vitamin E can enhance cognitive ability in elderly women

A researcher wishes to determine if vitamin E supplements could increase cognitive ability among elderly women. In 2021 the researcher recruited a sample of elderly women aged 50-65. At the time of the enrolment into the study, the women were randomised to either take Vitamin E, or a placebo for six months. At the end of the six-month period, the women were given a cognition test. Higher scores on this test indicate better cognition. The mean and standard deviation of the test scores of 400 women who took vitamin E supplements was 20 and 5 respectively. The mean and standard deviation of the test scores of the 500 women who took placebo supplements was 25 and 2, respectively.   REQUIRED: Construct a 99% confidence interval for the mean difference in cognition test scores between Vitamin E and placebo groups. Interpret your answer.         Describe the effect on the confidence interval in (a) women who took vitamin E supplements increased to 600 and those who took placebo supplements increased to 750 women assuming other measurements remained constant.             What are the limitations to this study for drawing conclusions about whether or not vitamin E can enhance cognitive ability in elderly women

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 58E: What is meant by the sample space of an experiment?
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A researcher wishes to determine if vitamin E supplements could increase cognitive ability among elderly women. In 2021 the researcher recruited a sample of elderly women aged 50-65. At the time of the enrolment into the study, the women were randomised to either take Vitamin E, or a placebo for six months. At the end of the six-month period, the women were given a cognition test. Higher scores on this test indicate better cognition. The mean and standard deviation of the test scores of 400 women who took vitamin E supplements was 20 and 5 respectively. The mean and standard deviation of the test scores of the 500 women who took placebo supplements was 25 and 2, respectively.

 

REQUIRED:

  1. Construct a 99% confidence interval for the mean difference in cognition test scores between Vitamin E and placebo groups. Interpret your answer.        
  2. Describe the effect on the confidence interval in (a) women who took vitamin E supplements increased to 600 and those who took placebo supplements increased to 750 women assuming other measurements remained constant.            
  3. What are the limitations to this study for drawing conclusions about whether or not vitamin E can enhance cognitive ability in elderly women?
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