Question

students at a local college were asked about their favorite subject in school and whether they prefer online classes, hybrid classes, or face-to-face classes. The table below summarizes the students responses: OnTine HybridFace-to-face Math 15 20 Science 55 215 History 25 30 120 45 175 Art 5 Other 85 10 2.噐 ret TeheËrmous probl鍔percent of resident : The vice president of instruction at this college believes that 15 percent of the students prefer onlne CTasses, 40 percent prefer hybrid classes, and 45 percent prefer face-to-face classes. You wi1l use a 0.10 level of significance to test the vice president's belief. a. Name the type of test that will allow you to address the vice president's question. (1 pt) e the table below by filling,in the observed frequ the previous problem! plat for each category. Refer to the table irn (3 pts) Hybrid Face-to-Face on Tine c. calculate the expected frequency for the students who prefer face-to-face classes. Please show your work. (3 pts) d. Give the value of the test statistic (you do not need to show your work) and use the appropriate table to find the critical value. (2 pts) e. Sraef youe decision regarding the null hypothesis and write a conclusion. (2 pts)

Answer 1

a) We will perform a Chi-square Goodness-of-fit Test.

b) Observed Frequency:

Online	Hybrid	Face-to-face
185	275	540

c) Expected frequency:

Online	Hybrid	Face-to-face
1000*0.15 = 150	1000*0.40 = 400	1000*0.45 = 450

d) Test statistic:

8.167 + 39.063 + 18 65.229 Ei 2=1

df = 3-1 =2

Critical value, χ²α = CHISQ.INV.RT(0.10, 2) = 4.605

e) Reject the null hypothesis.

There is not enough evidence for the beliefs of the vice presidents at 0.10 level of significance.