8/23/2015Slide 1 The introductory statement in the question indicates: The data set to use: GSS2000R.SAV The task to accomplish: a one-sample test of a population proportion The variable to use in the analysis: favor or oppose death penalty for murder [cappun] The population proportion to use in the comparison with our sample: 22% The alpha level of significance for the hypothesis test: 0.05

8/23/2015Slide 2 The first statement asks about the level of measurement. The SPSS Binomial test only works if the variable is dichotomous.

8/23/2015Slide 3 To determine the level of measurement, we examine the information about the variable. Select the Variables command from the Utilities menu.

8/23/2015Slide 4 Scroll down the list of variables to locate cappun. "Favor or oppose death penalty for murder" [cappun] contains two categories that do not represent missing data. The variable is dichotomous, satisfying the requirement to use the SPSS Binomial Test. Close the dialog box when we are finished.

8/23/2015Slide 5 "Favor or oppose death penalty for murder" [cappun] is dichotomous, satisfying the requirement to use the SPSS Binomial Test. Mark the check box for a correct answer.

8/23/2015Slide 6 If we had specified a variable that is not dichotomous, SPSS prints this message in the output. SPSS can compute the Binomial test for variables that have more than two categories if we recode the variable, or if we use the syntax version of the SPSS commands.

8/23/2015Slide 7 The next statement asks about the sample size. If we have 10 or more subjects in both the group that has the characteristic identified in the proportion and the group that does not have it, we can rely on the Central Limit Theorem to justify using probabilities based on the normal distribution. To answer this question, we compute the Binomial Test in SPSS.

8/23/2015Slide 8 To compute the one-sample test of a proportion in SPSS, select the Nonparametric Tests > Binomial test from the Analyze menu.

8/23/2015Slide 9 First, move the variable cappun to the Test Variable List. Second, enter the test proportion stated in the problem (from previous research). Third, click on the OK button to produce the output.

8/23/2015Slide 10 The sample size is large enough to make the sampling model for the sample proportions approximately normal based on the Central Limit Theorem if there are 10 or more cases in each of the categories compared in the test. There were 67 in the category "survey respondents who opposed the death penalty for persons convicted of murder" and 171 in the other category "survey respondents who favored the death penalty for persons convicted of murder". Both groups used to test the hypothesis had the required minimum of 10 cases. The sample size requirement is satisfied.

8/23/2015Slide 11 Both groups used to test the hypothesis had the required minimum of 10 cases. The sample size requirement is satisfied. Mark the check box for a correct answer.

8/23/2015Slide 12 The next questions asks us about the size of the proportion of cases in the target category, “opposed.”

8/23/2015Slide 13 The correct percentage of survey respondents in the category opposed in our sample was 28.2%, which SPSS rounds off to.28.

8/23/2015Slide 14 The correct percentage of survey respondents in the category opposed in our sample was 28.2%. Mark the check box for a correct answer.

8/23/2015Slide 15 The next statement asks us what the null hypothesis for the test states.

8/23/2015Slide 16 The population proportion is given in the statement of the problem.

8/23/2015Slide 17 This is the value entered in the Test Proportion text box, i.e This is the also the value that SPSS prints in the output table.

8/23/2015Slide 18 The null hypothesis for the test states that the true proportion of survey respondents who opposed the death penalty for persons convicted of murder is equal to the population proportion, which in this problem is the proportion cited in previous research, Mark the check box for a correct answer.

8/23/2015Slide 19 The next statement asks us about the probability (p-value or sig. value) for the test of a population proportion.

8/23/2015Slide 20 The probability that the proportion in our sample was different from the proportion reported in previous research was p =.031. The probability for the two-tailed test is computed by doubling the probability of the one-tailed test reported in the SPSS output (2 x.015 =.031). SPSS computes the one-tailed probability for the test. To get the two-tailed probability, we double this number.

8/23/2015Slide 21 The probability that the proportion in our sample was different from the proportion reported in previous research was p =.031. Mark the check box for a correct answer.

8/23/2015Slide 22 The next statement asks about the statistical decision or conclusion that we would make based on the p-value.

8/23/2015Slide 23 When the p-value for the statistical test is less than or equal to alpha, we reject the null hypothesis and interpret the results of the test. If the p-value is greater than alpha, we fail to reject the null hypothesis and do not interpret hypothesis. The p-value for this test (p =.031) is less than or equal to the alpha level of significance ( p =.050) supporting the conclusion that we reject the null hypothesis. Mark the check box for a correct answer.

8/23/2015Slide 24 The final statement asks us to interpret the results of the statistical test.

8/23/2015Slide 25 Since we rejected the null hypothesis and since the proportion of survey respondents who opposed the death penalty for persons convicted of murder in our sample is actually larger than the proportion reported in research, it is reasonable to suggest that actual proportion of survey respondents who opposed the death penalty for persons convicted of murder in the population has increased. We mark the check box for a correct answer. When we do not reject the null hypothesis, we do not interpret the results.

8/23/2015Slide 26 If we did not satisfy the level of measurement or the sample size, we should not use the test or its results. We would not mark any of the check boxes and None of the above would be the correct answer.

8/23/2015Slide 27 Yes Target variable is dichotomous? Yes Do not mark check box. Mark statement check box. No 10+ subjects in target and other categories? Do not mark check box. No Mark statement check box. Mark only “None of the above.” Stop. We do not mark “None of the above” because level of measurement should be marked if we got to this step.

8/23/2015Slide 28 Yes Proportion in sample stated correctly? Yes Do not mark check box. Mark statement check box. No Do not mark check box. No Mark statement check box. H 0 : proportion = proportion from previous research

8/23/2015Slide 29 Yes P-value (sig.) stated correctly? Yes Do not mark check box. Mark statement check box. No Do not mark check box. No Mark statement check box. Reject H 0 is correct decision (p ≤ alpha)? Stop. For two-tailed test, we double the one-tailed p-value output by SPSS. We interpret results only if we reject null hypothesis.

8/23/2015Slide 30 Interpretation is stated correctly? Yes Do not mark check box. Mark statement check box. No