2a. Are the variances of the unemployment percentages similar for Texas and Oklahoma? First calculate by hand the ratio of the larger variance to the smaller variance. Are the variances similar given the criterion for equal variances presented in class? Explain. How can you tell from your computer output? Which set of t-test results should you then use? Explain why. Does it make any difference in your analysis which set of t-test results you use? Explain why or why not. 2b. Regardless of whether the variances are equal or unequal, assume the variances are equal and use that formula to work out the t-test problem by hand. State the research and null hypothesis that SPSS uses. What table value do you use to set up an initial rejection region at the .05 level? Show how you obtained the degrees of freedom needed to obtain the correct t-value. 2c. Use the standard deviations from your computer output to calculate the standard error of the difference between the two means. Work out your computations to at least 4 places to the right of the decimal point. Calculate the t-test. Your obtained t-test should be very similar to that from your computer output. If not, check your hand computations until your answer is similar to that of your output. ID name unemployed 26 Enid 13.6 27 Lauton 16.7 28 Oklahoma City 7.1 29 Tulsa 8.9 PLEASE SHOW WORK & DETAILED INTERPRETATION 2d. Interpret your findings answering the following questions in order to explain what the statistical test tells you about the nature of the difference between Texas and Oklahoma metropolitan unemployment. Explain why you reject or do not reject the null hypothesis. If you do reject the null hypothesis, what is the probability of making a Type 1 error according to the t-table in APPENDIX C? What is the level of statistical significance given in your computer output? If you found a statistically significant difference, what is the nature of the difference between the mean unemployment percentages of the two states? 2e. Calculate a 95% confidence interval for the true difference between the state MSA unemployment percentages. Again, assume the variances are equal. Use the information from your computer output to show how the upper and lower boundaries of the confidence interval were obtained. Interpret the value of the confidence interval for the difference in state MSA unemployment percentages. What does the confidence interval specifically tell you about the difference in state MSA unemployment percentages?

Group Statistics Std. Sid. Error state N Mean Deviation Mean punempl 25 8.204 2.1935 4387 2 4 11.575 4.3798 2.1899 Independent Samples Test Levene's i-test Test for for Equality Equality of of Variances Means purtempl Equal 7.341 012 -2.473 27 variances F Sig assumed Equal variances -1.509 3.245 not assumed Independent Samples Test I-test for Equality of Means 95% Confidence Interval of the Mean Std. Error Difference Sig. (2-tailed) Difference Difference Lower punempl Equal variances 020 -3.3710 1.3632 -6.1681 assumed Equal variances 222 3.3710 2.2334 -10.1846 not assumed Independent Samples Test I-test for Equality of Means 95% Confidence Interval of the Difference Upper punempl Equal variances assumed - .5739 Equal variances not assumed 3.4426