Question

After a losing season, there is a great uproar to fire the head football coach. In a random sample of 220 college alumni, 77 favor keeping the coach. Test at the 0.05 level of significance whether the proportion of alumni who support the coach is less than 50%. (a) State the null hypothesis and the alternate hypothesis to test whether the proportion of alumni who support the coach is less than 50%. (Round your answers to 2 decimal places.)
H0: π ≥ _______ H1: π < _______

(b) State the decision rule for 0.05 significance level. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)
Reject H0 if z is < _______

(c) Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

(d) Test at the 0.05 level of significance whether the proportion of alumni who support the coach is less than 50%. (Reject OR Do Not Reject) H0. There is (sufficient OR insufficient) evidence to conclude the population proportion of alumni supporting the coach is less than 0.50.

Answer 1

H0: π ≥ __0.50_ H1: π < __0.50_

b)

Reject H0 if z is < -1.64

c)

test stat = z                =

(p̂-p)/Se=

-4.450

d)Reject Ho ,

There is sufficient   evidence to conclude the population proportion of alumni supporting the coach is less than 0.50.