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Cal Poly STAT 217 - Using Minitab

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Using Minitab Choose Stat ¾ Basic Statistics ¾ 2-Sample t If have a data file of individual observations: • If data are “stacked” use “Samples in one column” option • If data are “unstacked” use “Samples in different columns” option If have descriptive statistics output: Use “Summarized data” and specify the sample sizes, sample means, and smaple standard deviations. Do no check “Assume equal variances” box. Using Java applet (if only given summary statistics)Select two means option • Specify direction of alternative and hypothesized difference • Enter smaple mean, sample standard deviation, and sample size for each group, press Calculate Practice: Marriage Ages Listed below are the ages of a sample of 24 couples taken from marriage licenses filled in Cumberland County, Pennsylvania, in June and July 1993. couple husband wife couple husband wife couple husband wife 1 25 22 9 31 30 17 26 27 2 25 32 10 54 44 18 31 36 3 51 50 11 23 23 19 26 24 4 25 25 12 34 39 20 62 60 5 38 33 13 25 24 21 29 26 6 30 27 14 23 22 22 31 23 7 60 45 15 19 16 23 29 28 8 54 47 16 71 73 23 35 36 (a) Produce numerical and graphical summaries to compare the sample of wife ages to the sample of husband ages. (b) Carry out a two-sample t-test to determine whether these sample means indicate a statistically significant difference in the population means. (c) Are the technical conditions for the above procedure met? Hint: What are the observaitonal units? (d) Is there evidence that the husband is older than the wife in a majority of couples?Solution (a) Both distribuitons are slightly skewed to the right. There is one wife that is identified by Minitab to be an outlier (couple 16). The husband’s ages appear slightly higher than the wife’s ages. The spread of the two distributions are similar (s1=13.56 years and s2=14.56 years). (b) From Minitab (Stat > Basic Statistics > 2-Sample t) Two-sample T for hus age vs wife age N Mean StDev SE Mean hus age 24 35.7 14.6 3.0 wife age 24 33.8 13.6 2.8 Difference = mu hus age - mu wife age Estimate for difference: 1.88 95% lower bound for difference: -4.95 T-Test of difference = 0 (vs >): T-Value = 0.46 P-Value = 0.323 Based on the above output we would fail to reject H0, there is not statistically significant evidence of a difference in the two population means. However, we do not meet the technical conditions! These are not two independent samples, but one set of couples. There is a definite relationship between members of these samples! We just have one sample of 24 couples, this is a matched pairs design. Thus, the appropriate analysis is to compute the differences for each couple. The sample mean age difference is x = 1.875 years with standard deviation s =4.812 years. The distribution is mostly symmetric with one outlier at 15 year age difference (couple 7). Assuming these 24 couples of representative of the population of Pennsylvania marriages: Let μ = mean difference in age (husband – wife) H0: μ = 0 (same age on average) Ha: μ > 0 (husband tends to be older)Using a one-sample t-test in Minitab (Stat > Basic Statistics > 1-Sample t) Variable N Mean StDev SE Mean age diff 24 1.875 4.812 0.982 Variable 95.0% Lower Bound T P age diff 0.191 1.91 0.034 At the 5% level, we would reject H0 and conclude that there is significant evidence that μ > 0, that the average age difference is positive, indicating that the husband tends to be older than the wife. A 90% confidence interval (from Minitab) tells us that the mean age difference is between .191 years and 3.56 years. (c) Now the variable is whether or not the husband is older which is categorical. So instead of means, we work with proportions. Let = proportion of all PA couples with the husband older pˆ = 16/24 = .667 H0: = .5 Ha: > .5 (a majority of couples has the husband older) Technical conditions: Assuming SRS and .5(24)=12>10. From Minitab (Stat > Basic Statistics > 1 Proportion) Test of p = 0.5 vs p > 0.5 Sample X N Sample p 90.0% Lower Bound Z-Value P-Value 1 16 24 0.666667 0.543349 1.63 0.051 This also indicates that there is some evidence (though not significant at the 5% level) that the husband is older in a majority couples in this population.Summary: • Thoroughly check your technical conditions. In particular, discussthe normality of the sample data if you are working with quantitative data and have small sample sizes • Remember, if the data are “paired” you need to examine the differences and do a one-sample procedure • Make sure you are consistent in how you define group 1 and group 2 and the direction of your alternative (Ha: μ1-μ2 > 0 usually ends up with t> 0). • It is important to remember all earlier lessons: start with graphical and numerical summaries (include them and discuss them), check technical conditions, make sure your hypothesis statements are about the parameter(s), interpret the p-value and confidence the same way, consider the study design when deciding if you can draw cause-and-effect conclusions or if you can generalize from the sample to a larger population. • Also realize that even when there is a statistical tendency it is certainly not the case that every member of one group is higher than every member of the other group. Men tend to be taller than women, but there are cetainly some women who are taller than most men. Statistical tendencies pertain to average or typical cases but not necessarily to individual cases. • I hope you will take care of the technology and let Minitab and/or the java applet do the calculations for you, allowing you to focus on selecting the appropriate procedure and interpreting the resulting


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Cal Poly STAT 217 - Using Minitab

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