QMS202 W18 Lecture 12 Review.pdf - QMS202 Business...

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QMS202 Business Statistics IILecture 12
EX A physician is evaluating a new diet for her patients with a family history of heart disease.To test the effectiveness of this diet, 16 patients are placed on the diet for 4 months. Their weights and triglyceride levels are measured monthly starting before the study, and the physician wants to know if either set of measurements has changed. USE tgo and tg4 data only. QUESTION: Is there a difference between the before and after TGL levels?QMS 202 W18 Lecture 122
Across all 16 subjects, triglyceride levels dropped between 14 and 15 points on average after 4 months of the new diet.
NOW ADD SOME WEIGHT DATAQMS 202 W18 Lecture 123
•Across all 16 subjects, triglyceride levels dropped between 14 and 15 points on average after 4 months of the new diet•They lost weight too!The standard deviations for pre- and post-diet measurements reveal that subjects were more variable with respect to weight than to triglyceride levels.At -0.286, the correlation between the baseline and 4-month triglyceride levels is not statistically significant.
QMS 202 W18 Lecture 124
The Mean column in the paired-samples t test table displays the average difference between triglyceride and weight measurements before the diet and 4 months into the diet.The Std. Error Mean column provides an index of the variability one can expect in repeated random samples of 16 patients similar to the ones in this study.The 95% Confidence Interval of the Difference provides an estimate of the boundaries between which the true mean difference lies in 95% of all possible random samples of 16 patients similar to the ones participating in this study.The t statistic is obtained by dividing the mean difference by its standard error.
QMS 202 W18 Lecture 125
The Sig. (2-tailed) column displays the probability of obtaining a t- statistic whose absolute value is equal to or greater than the obtained t-statistic.Since the significance value for change in weight is less than 0.05, you can conclude that the average loss of 8.06 pounds per patient is not due to chance variation, and can be attributed to the diet. However, the significance value greater than 0.10 for change in triglyceride level shows the diet did not significantly reduce their triglyceride levels. The paired-samples t-test is appropriate whenever two related sample means are to be compared.
QMS 202 W18 Lecture 126
REVIEW: EX. Compare 2 related populations of averagewaiting times at 2 banks to see a Loan Officer, without an appointment .(α=.05)Measured by 2 paid Observers in 2 branches for a period of 15 days (average times on same days at both banks!). These are PAIRED SAMPLES!H0: μD=0 μ1=mean waiting time at CIBCH1: μD≠0 µ2=mean waiting time at BMOConclusion: Reject H0 because p= Sig=.0122< α=.05QMS 202 W18 Lecture 127
Using economy of data let us now assume that the populations are independent and that we want to test the hypothesis that the mean waiting time at the banks is equal.

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