Homework SourseSingle Sample ttest the florida department of corrections pu
Single Sample t-test.
the florida department of corrections publishes an online death row fact sheet. it reports the average time on death row prior to execution as 10.68 years for the 44 inmates executed prior to 2000.This mean is a paramour because it is calculated from the entire population of executed prisoners in Florida. Has time spent on death row significantly increased in recent years? According to the execution list linked to the same site, 10 prisoners executed in Florida during the years 2010 through 2013 spent: 24.2, 30.13, 17.03, 31, 26.4, 24.5, 32, 21, 24.6 and 35 years on death row, respectively.
1. are the data sufficient to conclude that time spent on death row increased in recent years? Use SPSS to complete hypothesis test with alpha = .05
2. what are the null and research hypothesis in symbols?
3. calculate effect size r2 and explain what it means
4. write a sentence describing the outcome of the hypothesis test, as it would appear in a published article.
Solution
1. Say, average time spent on death row is denoted by T.
Therefore, value of T for the sample of 10 prisoners executed in Florida from 2010 to 2013 is:
(24.2+30.13+17.03+31+26.4+24.5+32+21+24.6+35)/10 = 26.59
Standard Error of the sample = Standard Deviation of the sample / square root of sample size = 5.46 / 3.16 = 1.73
Therefore, the t-statistic to test the null hypothesis is calculated as (sample statistic - hypothesized value) / standard error = (26.59 - 10.68) / 1.73 = 9.206
At the 0.05 level of significance (i.e. alpha), the critical value for the two-sided t-test for 9 degrees of freedom (d.f. = sample size -1) is 2.262. Since our calculated t-statistic exceeds the critical value, we reject the null hypothesis at a 0.05 alpha level.
To perform this test in SPSS, take the 10 sample values in a column in the Data View window of SPSS. Click on Analyze à Compare Means à One-Sample T Test. Select the sample data as the test variable and the test value as 10.68 (i.e. the hypothesized value). Run the test.
In the output window, the Sig. (2-tailed) value is 0.000 < 0.05. Therefore, we reject the null hypothesis at a 0.05 alpha level.
2. The Null Hypothesis – H0: T = 10.68
The Research Hypothesis – H1 10.68
3. Effect size r2 = t2 / (t2 + degrees of freedom) = 9.2062 / (9.2062 + 9) = 0.90.
The effect size r2 of 0.90 indicates a very large effect. The sample mean of 26.59 is very different from 10.68.
4. From the hypothesis test conducted on the sample, we can conclude that time spent on death row increased in recent years, compared to the average prior to 2000.
