Students and catalog shopping What is the most important reason that students buy from catalogs?The answer may differ for different groups of students. Here are results for separate random samples of American and Asian students at a large midwestern university:26 American Asian Save time 29 10 Easy 28 11 Low price 17 34 Live far from stores 11 4 No pressure to buy 10 3 (a) Should we use a chi-square test for homogeneity or a chi-square test for independence in this setting? Justify your answer. (b) State appropriate hypotheses for performing the type of test you chose in part (a). Minitab output from a chi-square test is shown below. Chi-Square Test: American, Asian Expected counts are printed below observed counts Chi-Square contributions are printed below expected counts American Asian Total 1 29 10 39 23.60 15.40 1.236 1.894 2 28 11 39 23.60 15.40 0.821 1.258 3 17 34 51 30.86 20.14 6.225 9.538 4 11 4 15 9.08 5.92 0.408 0.625 5 10 3 13 7.87 5.13 0.579 0.887 Total 95 62 157 Chi-Sq = 23.470, DF = 4, P-Value = 0.0001 (c) Check that the conditions for carrying out the test are met. (d) Interpret the P-value in context. What conclusion would you draw?

STAT-5615: Statistics in Research I Lecture 10 z-tests for Proportions Ott & Longnecker Ch 10.2, 10.3 Dr. Christian Lucero Virginia Tech Fall 2016 One Sample Hypothesis Test for the Population Proportion Many applications in health related research involve population proportions. I What proportion of the population smoke cigarettes I What proportion of the population has health insurance Estimating the population proportion (p) is similar to estimating the population mean. A sample is drawn and the sample proportion p is computed. Under the Central Limit Theorem, the sample proportion, p , has an approximate normal distribution with a mean p and a standard error r p(1▯