Question

Use the GSS dataset to answer the questions below. All analysis must be completed using your own GSS data set. Failure to use your own GSS data set will result in a zero for the question. As above, you will need to read and interpret the question to determine which statistical test is appropriate, as well as whether it is a one-tailed or two-tailed test. Similar to the questions above, you must: 1. State the null and research hypotheses 2. Provide the Z(critical), T(critical), or χ2 (critical) score corresponding to the α thresh- old for your test 3. Explicitly provide your test statistic that is in your SPSS output (the exception is for tests of proportion, as the test statistic is not returned by SPSS) 4. Provide your decision about statistical significance You should also substantively interpretthe results of your test (again, keep it short). All of the necessary SPSS output must be pasted into your document. 3. Is educational attainment independent from gender in the GSS? To answer this question, first start by recoding the variable EDUC into a new variable with categories for respondents who have completed the 12th grade or less, and respondents who have at least some college or more education. You will also need to use the variable SEX. Can you conclude that the two variables are independent at 99.9% level of confidence (10 points)

Answer 1

1)

Ho:X =  $\mu$

Ha:X$\neq$$\mu$

2)

Z CRITICAL VALUE IS 2.58 FOR TWO TAIL TEST

T CRITICAL VALUE IS 2.58 FOR TWO TAIL TEST

t-test = (sample mean - population mean)/ standard error

= (39.75-40)/0.518

= -0.481695568

so accept the null hypothesis because of calculated t value is less than critical t (2.58) value so, there is no significant evidence that sample mean and population mean are different .

confidence interval = mean $\pm$ t * se

= 39.75 $\pm$ 2.58 * 0.519

= 39.75 $\pm$ 1.33902

lower = 38.41098 to upper = 41.08902