Suppose a sample of 20 subjects participated in a weight loss program. To evaluate the program, the
Question:
Suppose a sample of 20 subjects participated in a weight loss program. To evaluate the program, the weight of each person was measured before the program begins and 6 months later. Suppose that we observe a mean difference in weight (i.e. weight before the program minus weight after the program) equal to 8.3000 pounds and a standard deviation equal to 7.1826 pounds. [Note: Don?t round too soon in the calculation. Report four decimal places in questions 1, 2 and 3]
1) Before calculating the 95% confidence interval, it is always a good plan to first identify the values of the elements in the formula in order to complete the calculation. From Dawson and Trapp, we know that the formula for a 95% confidence interval for a mean difference is: Difference ? Confidence factor of the difference x Standard error.
Based on the information provided in the Part One scenario, what are the values for the difference, the confidence factor of the difference, and standard error? [Note: You will need to refer to Table A-3 in the textbook to help select the confidence factor. Also, you will need to calculate standard error using the values provided in the Part One scenario. Finally, always use a ?0.05 area in two tails? in this class unless otherwise told.]
2) Now that you have those values, calculate the 95% confidence interval (CI). What is the lower and upper bounds of that interval? [Show your work.]
3) Interpret this 95% CI.
4) As an added bonus, CIs can also be used to test a null hypothesis. In this scenario, we are told that the weights of participants were measured at the beginning and then again 6 months later. Let us assume that the null hypothesis states that the mean difference in weight will be zero. Consider the 95% CI that you calculated in question 2 above. Does the null value fall inside or outside of that 95% CI? Based on that, would you Reject or Fail to Reject the null hypothesis?
5) Dawson and Trapp discuss the similarities between hypothesis testing and confidence intervals and highlight one noticeable benefit of reporting confidence intervals. According to the authors of our textbook, what is the additional insight that CIs provide that hypothesis testing does not?
Statistics for Business & Economics
ISBN: 978-1337901062
14th edition
Authors: David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, James J. Cochran