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Comparing more than one sample In this lesson we will learn how to compare two groups. There are three t-tests available comparing two groups. a. Independent samples with unequal variance b. Independent sample with equal variance or pooled t-test. c. Paired data or repeated measures In part c, we measure a variable on same object or subject at two different times or locations. In part a and b two samples must be independent of each other. For these t-tests we assume the data is continuous and form a normal distribution. The data set vitals.xlsx contains body temperature, pulse and gender of 50 people who were subjected to stress situations. Open this data set in MINITAB. And do the following. 1. Draw box plots of body temperature and pulse by gender. Are there any outliers? Save the project file and worksheet regularly. Type you name in the title of each graph. There re two outliers for female body temperatures. Male Female 90 85 80 75 70 65 60 Gender Pulse Boxplot of Pulse by Emily Meyer Male Female 101 100 99 98 97 96 Gender BodyTemp Boxplot of BodyTemp by Emily Meyer 2. Is it reasonable to assume that the body temperature and pulse are normally distributed? Give evidence to support your answer. The p-vale is 0.527 which is larger than 0.05, therefore the body temp is probably normally distributed. For the pulse the p-value is 0.704 which is larger than 0.05 therefore pulse is probably normally distributed. 101 100 99 98 97 96 99 95 90 80 70 60 50 40 30 20 10 5 1 Mean 98.26 StDev 0.7653 N 50 AD 0.318 P-Value 0.527 BodyTemp Percent Normality Test by Emily Meyer Normal 90 85 80 75 70 65 60 99 95 90 80 70 60 50 40 30 20 10 5 1 Mean 74.4 StDev 6.440 N 50 AD 0.258 P-Value 0.704 Pulse Percent Normality Test by Emily Meyer Normal

3. Display mean median quartiles, standard deviation of body temperature and pulse rate for males and females. 4. Conduct an independent sample unequal variance t-test to determine whether body temperatures under stress are different for males and females. State your conclusion so that non statistician can understand it. Null hypothesis: There is no difference in stressed body temperatures between males and females. Alternative hypothesis: Body temperatures under stress are different for males and females. The p-vale is 0.422 that means that it is greater than 0.05 so we cannot reject the null hypothesis. There is not enough evidence to say the males and females have different body temperatures under stress. 5. Find the 98% confidence interval for the difference between mean body temperature under stress between males and females. Interpret your results. 98% confidence interval is -0.348 to 0.700. We are 98% confidence that the difference of mean body temp under stress for females and males is between -0.348 degrees and 0.700 degrees.

9. Conduct a test to determine the homogeneity of variance of pulse rate between males and females. Null hypothesis: Variance of stressed pulse rate for females is the same as males Alternative hypothesis: Variance of stressed pulse rate for females is different from males The p-vale is 0.018 (0.031) is less than 0.05 so we reject the null hypothesis because there is evidence to say variance of pulse rate under stress for females is different from the males. 10. Use an appropriate test determine whether pulse rates are different for males and females. State your conclusion so that non-statistician can understand it. Use unequal variance independent sample t-test Null hypothesis: there is no difference in stressed pulse rate between males and females Alternative hypothesis: pulse rate under stress is different for males and females. The p-value is 0.795 and that is greater than 0.05 so we cannot reject the hull hypothesis because there is not enough evidence to say the pulse rate under stress for females is different from males. Upload the worksheet and MINITAB project file to D2L. P-Value 0.018 P-Value 0.031 Bonett’s Test Levene’s Test Male Female 90 85 80 75 70 65 60 Gender Levene Bonett 7 6 5 4 3 2 1 Male Female 120 100 80 60 40 20 0 Gender Boxplot of Pulse vs Gender 95% CI for σ²(Female) / σ²(Male) 95% CI for σ² Test and CI for Two Variances: Pulse vs Gender by Emily Meyer Ratio = 1 vs Ratio ≠ 1