Question

After a college football team once again lost a game to their archrival, the alumni association conducted a survey to see if alumni were in favor of firing the coach. a simple random sample of 100 alumni from the population of all living alumni was taken. 64 of the alumni in the sample were in favor of firing the coach. let p represent the proportion of all living alumni who favored firing the coach. suppose the alumni association wished to see if the majority of alumni are in favor of firing the coach. denote p true as the true(population) proportion of all living alumni who favor firing the coach.

A) what hypotheses should one test if one suspects that p true is less than 70%?
a) H0: ptrue<0.7; Ha:ptrue=0.7
b) H0: ptrue=0.7; Ha:ptrue<0.7
c) H0: ptrue\\eq0.7; Ha:ptrue>0.7
d) H0: ptrue=0.7; Ha:ptrue>0.7
e) H0: ptrue\\eq0.7; H a:ptrue=0.7
B) What is the P-value, P associated with the test statistic for the test in part A)?
a) 0.0476
b) 0.1902
c) 0.0951
d) 0.64
e) 0.06
C) Is it reasonable to conclude that Ptrue is less than 70%? Use a significant level of 10%.
a) YES
b) NO

Answer 1

A)

a) H0: ptrue < 0.7; Ha: ptrue = 0.7

B)

d) 0.64

C)

b) No

Explanation:

Hypothesis is a technique which is used to test the event against an alternative hypothesis. The null hypothesis is set as a basis which is tested against an alternative hypothesis to make a conclusion. This null hypothesis is analysed against a probability using significance level and then a conclusion is made to accept or reject the null hypothesis.