Question

In a particular year, 68% of online courses taught at a system of community colleges were taught by full-time faculty. To test if 68% also represents a particular state's percent for full-time faculty teaching the online classes, a particular community college from that state was randomly selected for comparison. In that same year, 31 of the 44 online courses at this particular community college were taught by full-time faculty. Conduct a hypothesis test at the 5% level to determine if 68% represents the state in question.

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

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

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

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

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

(i) Alpha:
α =

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

Answer 1

Given : n=44 , X=31 , The sample proportion , p=X/n=31/44=0.7056

Hypothesis : Vs  

A) We use the normal distribution.

Where , and  

B) The test statistic is ,

C) p-value=

; From standard normal distribution table

D) Decision : Here , p-value=0.7188 >

Therefore , do not reject Ho

Conclusion : Hence , there is sufficient evidence to support the claim that the 68% also represents a particular state's percent for full-time faculty teaching the online classes.

F) The 95% confidence interval for the true proportion is ,

Where ,   ; From standard normal distribution table