Use the data from the 2014 General Social Surveys in the file gss_2014.Rdata

(available on the course website).These data are a random sample from the adult population in the US. Be sure to allow enough time to do the analyses, calculate the necessary additional statistics, and interpret the results.Use alpha=.05 for the significance level.

Variable

Highest year of school completedEDUC

1.Draw a boxplot to show the distribution of number of years of education completed. Label the y-axis of the graph. Provide a title for the graph that has your name and student ID number. For example:Peter the Anteater 12345678

DATA

> numSummary(Dataset[,"EDUC", drop=FALSE], statistics=c("mean", "sd",

+"se(mean)", "IQR", "quantiles"), quantiles=c(0,.25,.5,.75,1))

meansdse(mean) IQR 0% 25% 50% 75% 100%nNA

13.69925 3.071283 0.0609760940 121416 20 25371

> with(Dataset, (t.test(EDUC, alternative='two.sided', mu=0.0,

+conf.level=.95)))

One Sample t-test

data:EDUC

t = 224.67, df = 2536, p-value < 2.2e-16

alternative hypothesis: true mean is not equal to 0

95 percent confidence interval:

13.57968 13.81882

sample estimates:

mean of x

13.69925

> with(Dataset, (t.test(EDUC, alternative='two.sided', mu=0.0,

+conf.level=.05)))

One Sample t-test

data:EDUC

t = 224.67, df = 2536, p-value < 2.2e-16

alternative hypothesis: true mean is not equal to 0

5 percent confidence interval:

13.69543 13.70308

sample estimates:

mean of x

13.69925

2.Find the 95% confidence interval for the mean years of school completed (EDUC).

a.Report the mean years of school completed.

b.Report the lower and upper limits of the interval

c.Describe in words what this confidence interval indicates about the mean years of school completed.

3. Suppose that your reading of professional research on the topic leads you to expect that, due to rising numbers of people pursing a college or university education, on average adults in the US have completed 13.5 years of schooling, rather than completing more or less than that amount.Use the variable highest year of school completed (EDUC) to investigate this hypothesis.

a.State the null hypothesis in words and in symbols

In words

In symbols

b.State the alternative hypothesis in words and in symbols

In words

In symbols

c.Are you using a directional or non-directional alternative hypothesis?Explain why you are using that kind of hypothesis.

d.Find the test statistic (t) for this significance test.Report the value of t, the degrees of freedom (df), and the P value that R reports

t statistic =

degrees of freedom =

P value from R =

(Report this to 3 decimal places.)

e.Is the P value reported by R appropriate for the test that you are doing, or not?Explain why or why not it is correct.If it is not correct, what P value should you use instead?

f.Using a .05 significance level (alpha) what do you decide about the null hypothesis?

g.Could your decision about the null hypothesis (question 2f) be wrong?If so, how and why could it be wrong?

h.Briefly, what does your decision about the null hypothesis indicate about the mean years of schooling completed in the US population?

4. summarize the results of your statistical analyses of the mean years of schooling completed by adults in the US.You should briefly describe the data and report the sample mean, the confidence interval, the t test for the mean (with the t statistic, degrees of freedom, p value, and significance level (alpha) that you used for your significance test).Be sure to include your hypotheses and your decision about the null hypothesis.Finally, provide a substantive conclusion about the highest year of schooling completed by adults in the US.