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This document provides sample data and examples for statistical hypothesis testing. It includes data on gender and ice cream flavor preferences, weight gain in cattle, online purchasing habits of graduate students, life satisfaction scores in older and younger adults, heart rate before and after meditation, and US history exam scores by college major. Statistical tests described include z-test, t-test, and ANOVA. The document serves as a reference for how to set up and analyze different types of statistical hypothesis tests using example data sets.
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- 1. Once the difference scoresare obtained,all furtherstatisticsare calculatedusingthese scores insteadof the pretest/posttestor before /afterscoresBefore AfterDSubject(x1) (x2) (x2 - x1) 1 2 8 6 2 0 4 4 3 4 11 7 4 2 5 3 5 3 8 5 ∑ D = 25 Let's try an example. 500 elementary school boys and girls are asked which is their favorite color: blue, green, or pink? Results are shown below: In this example, we seek to determine whether or not there is an association between gender and preference for ice cream flavour – these are the 2 categorical variables of interest. Gender has 2 categories: ? Men ? Women Ice cream flavour has 3 categories: ? Chocolate ? Vanilla ? Strawberry My data come from a hypothetical survey of 920 people that ask for their preference of 1 of the above 3 ice cream flavours. Here are the data: Flavour Chocolate Vanilla Strawberry Total
- 2. Gender Men 100 120 60 280 Women 350 200 90 640 450 320 150 920 Single mean A herd of 1,500 steer was fed a special high‐protein grain for a month. A random sample of 29 were weighed and had gained an average of 6.7 pounds. If the standard deviation of weight gain for the entire herd is 7.1, test the hypothesis that the average weight gain per steer for the month was more than 5 pounds. Population An e-commerce research company claims that 60% or more graduate students have bought merchandise on-line.A consumer group is suspicious of the claim and thinks that the proportion is lower than 60%. A random sample of 80 graduate students show that only 22 students have ever done so. Is there enough evidence to show that the true porportion is lower than 60%? A research study was conducted to examine the differences between older and younger adults on perceived life satisfaction. A pilot study was conducted to examine this hypothesis. Ten older adults (over the age of 70) and ten younger adults (between 20 and 30) were give a life satisfaction test (known to have high reliability and validity). Scores on the measure range from 0 to 60 with high scores indicative of high life satisfaction; low scores indicative of low life satisfaction. The data are presented below. Compute the appropriate t-test. Older Adults Younger Adults 45 34 38 22 52 15 48 27 25 37
- 3. 39 41 51 24 46 19 55 26 46 36 Mean = Mean = S = S = S2 = S2 = Example ? Doesmeditationinfluence stress??Measure heartrate as an indicatorof stress before andaftermeditation575 70 4 81 73 3 80 71 2 78 71 1 70 71 SubjectX1X2 Before After A researcher is concerned about the level of knowledge possessed by university students regarding United States history. Students completed a high school senior level standardized U.S. history exam. Major for students was also recorded. Data in terms of percent correct is recorded below for 32 students. Compute the appropriate test for the data provided below. Education Business/Management Behavioral/Social Science Fine Arts 62 72 42 80 81 49 52 57 75 63 31 87 58 68 80 64 67 39 22 28 48 79 71 29 26 40 68 62 36 15 76 45