Exam 11: Chi-Square and Analysis of Variance

Test the claim that the samples come from populations with the same mean. Assume that the populations are normally distributed with the same variance. -Given the sample data below, test the claim that the populations have the same mean. Use a significance level of 0.05. Brand A Brand B Brand C n=10 n=10 n=10 =32.9 =31.6 =27.1 =3.16 =3.04 =4.66

A survey conducted in a small town yielded the results shown in the table. Men Women Plan to vote 105 87 Do not plan to vote 312 246 i) Test the claim that the intention to vote in the next presidential election is independent of the gender of the person being surveyed. Use a 0.05 significance level. ii) Using Yates' correction, replace $\sum \frac{(\mathrm{O}-\mathrm{E})^{2}}{E}\text { with } \sum \frac{(|O-E|-0.5)^{2}}{E}$ and repeat the test. What effect does Yates' correction have on the value of the test statistic?

Test the claim that the samples come from populations with the same mean. Assume that the populations are normally distributed with the same variance. -The data below represent the weight losses for people on three different exercise programs. Exercise A Exercise B Exercise C 2.5 5.8 4.3 8.8 4.9 6.2 7.3 1.1 5.8 9.8 7.8 8.1 5.1 1.2 7.9 At the 1% significance level, does it appear that a difference exists in the true mean weight loss produced by the three exercise programs?

At the same time each day, a researcher records the temperature in each of three greenhouses. The table shows the temperatures in degrees Fahrenheit recorded for one week. Greenhouse \#1 Greenhouse \#2 Greenhouse \#3 73 71 67 72 69 63 73 72 62 66 72 61 68 65 60 71 73 62 72 71 59 i) Use a 0.05 significance level to test the claim that the average temperature is the same in each greenhouse. ii) How are the analysis of variance results affected if 8° is added to each temperature listed for greenhouse #3?

Explain the computation of expected values for contingency tables in terms of probabilities. Refer to the assumptions of the null hypothesis as part of your explanation. You might give a brief example to illustrate.