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, 35 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.

1.Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value.

2. 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

1. The hypothesis being tested is:

H0: p = 0.68

Ha: p ≠ 0.68

The sketch is:

The p-value is 0.1006.

Since the p-value (0.1006) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we cannot conclude that 68% of online courses taught at a system of community colleges were taught by full-time faculty.

2. The 95% confidence interval for the true proportion is between 0.6763 and 0.9146.

Observed	Hypothesized
0.7955	0.68	p (as decimal)
35/44	30/44	p (as fraction)
35.	29.92	X
44	44	n
	0.0703	std. error
	1.64	z
	.1006	p-value (two-tailed)
	0.6763	confidence interval 95.% lower
	0.9146	confidence interval 95.% upper
	0.1192	margin of error