In a particular year, 68% of online courses taught at a systemof community colleges were taught by full-time faculty. To test if68% also represents a particular state's percent for full-timefaculty teaching the online classes, a particular community collegefrom that state was randomly selected for comparison. In that sameyear, 31 of the 44 online courses at this particular communitycollege were taught by full-time faculty. Conduct a hypothesis testat the 5% level to determine if 68% represents the state inquestion.

Note: If you are using a Student's t-distribution for theproblem, you may assume that the underlying population is normallydistributed. (In general, you must first prove that assumption,though.)

A. State the distribution to use for the test. (Round yourstandard deviation to four decimal places.)
P' ~ ________ (________,_________)

B. What is the test statistic? (Round your answer to two decimalplaces.)

C. What is the p-value? (Round your answer to fourdecimal places.)

D. Indicate the correct decision (\"reject\" or \"do not reject\"the null hypothesis), the reason for it, and write an appropriateconclusion.

(i) Alpha:
α =

E. Construct a 95% confidence interval for the true proportion.Sketch the graph of the situation. Label the point estimate and thelower and upper bounds of the confidence interval. (Round youranswers to four decimal places.)