## Question

###### Sixty-eight percent of online courses taught at community colleges nationwide were taught by full-time faculty: To test if 68% also represents California percent for full-time faculty teaching the online classes Long Beach City College (LBCC} in California was randomly selected for comparison In the same year; 34 of the 44 online courses LBCC offered were taught by full-time faculty: Conduct hypothesis test at the 5% level to determine if 68% represents California. NOTE: For more accurate result

Sixty-eight percent of online courses taught at community colleges nationwide were taught by full-time faculty: To test if 68% also represents California percent for full-time faculty teaching the online classes Long Beach City College (LBCC} in California was randomly selected for comparison In the same year; 34 of the 44 online courses LBCC offered were taught by full-time faculty: Conduct hypothesis test at the 5% level to determine if 68% represents California. NOTE: For more accurate results use more California community colleges and this past year'$ data_ Note: If You are using 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:) Part (a} Part (b} Part (c) Part (d) State the distibution t use ior the test (Round your answers t0 four decimal places 0.68 0.32 Part (e) Part (f} What the p-value? (Round your answer to four decimal places_ 2675 Explain what the p-value means ior inis problem: If Hc is false, then there is chance equal to tne p-value that tne proportion of online courses taught by full-time faculty is not at least a5 different as the sample proportion from 6396 If Hc is true, then there iS chance equal to the p-value thai the proportion of online courses taugnt b} iull-time facuity not at least as different a5 ine sample proportion is irom 68%6_ # Ho true; then there chance equal to the p-value tha the proportion of online courses taugnt by iuli-time facuity is at least as different as the sample proportion is from 68%6. If Hc is false, then there is chance equal to ine p-value that ine proportion of online courses taught by full-time faculty is at least as different a5 ine sample proportion Tom 68%_ Part (g} Part (h} Part (i) Construct 9590 confidence interval for the true proportion Sketch the graph of the situation: Label the point estinate and ine lower ad upper bounds of the confidence interval. (Round your answers t0 four decimal olaces 95% CI 669