Two Independent Samples T-test

1. How many total respondents were there in 2003 ? How many total respondents were there in 2013? (SPSS provides N for each year).
2. Create a graph on Excel to show the average agreement and the standard error of the two years . Below the graph, describe if there may be a significant difference between the two years .
3. Describe each years’ means in reference to the ordinal value s. (Review slide 2 on the lab PowerPoint. Locate each years’ mean s on the scale, and describe where they land. For example, "slightly above neutral," "slightly below disagree," etc. ).
   The mean level of agreement in 2003 is 2.52, which is between disagree and neutral. The mean level of agreement in 2003 is 3.21, which is a bit above neutral.
4. You will now test whether two samples based on year are equal in their "agreement" rating or if there is a significant differ ence. The "treatments" here are ‘2003’ and ‘2013’ . Although these are not real "treatments," they are still independent variables that affect two different samples .
   1. Write notations for a null hypothesis and an alternative hypothesis for a two-tailed test.
   2. What is the t-value, the df, and the Sig. reported by SPSS for the Independent Samples Test (use the "Equal variances assumed" line and ignore the "Lavene’s Test for Equality of Variance" information )?
   3. Write out the statistical decision in notation using an alpha level of .01 (Use SPSS’ data; no need to hand-calculate information).
   4. Are you retaining or rejecting the null hypothesis?
   5. According to this test, might time have changed Americans’ opinion on gay marriage ? Explain.
   6. Calculate r ² . (Show your work on the SPSS printout). What effect size did time have on Americans’ opinions towards gay marriage ?
5. How many total females were surveyed overall? How many total males were surveyed overall? (SPSS provides N for each year).
6. Create a graph on Excel to show the average agreement and the standard error of the two genders. Below the graph, describe if there may be a significant difference between the two genders .
7. Describe each genders’ means in reference to the ordinal values. (Review slide 2 on the PowerPoint. Locate each genders’ means on the scale, and describe where they land. For example, "slightly above neutral," "slightly below disagree," etc.).
8. You will now test whether two samples based on gender are equal in their "agreement" rating or if there is a significant difference. The "treatments" here are ‘Female’ and ‘Male.’ Although these are not real "treatments," they are still independent variables that affect two different samples.
   1. Write notations for a null hypothesis and an alternative hypothesis for a two-tailed test.
   2. What is the t-value, the df, and the Sig. reported by SPSS for the Independent Samples Test (use the "Equal variances assumed" line and ignore the "Lavene’s Test for Equality of Variance" information )?
   3. Write out the statistical decision in notation using an alpha level of .01 (Use SPSS’ data; no need to hand-calculate information).
   4. Are you retaining or rejecting the null hypothesis?
   5. According to this test, is one gender more supportive of gay marriage than the other gender? Explain.
   6. Calculate r ² . (Show your work on the SPSS printout). What effect size does gender have on Americans’ opinions towards gay marriage?

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