After a losing season, there is a great uproar to fire the head football coach.

Question

After a losing season, there is a great uproar to fire the head football coach. In a random sample of 260 college alumni, 117 favor keeping the coach. Test at the .01 level of significance whether the proportion of alumni who support the coach is less than 50 percent.

State the null hypothesis and the alternate hypothesis. (Round your answers to 2 decimal places.)

State the decision rule for .01 significance level. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

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

Test at the .01 level of significance whether the proportion of alumni who support the coach is less than 50 percent.

(reject, do not reject) H0. There is (sufficient, insufficient) evidence to conclude the population proportion
of alumni supporting the coach is less than .50.

After a losing season, there is a great uproar to fire the head football coach. In a random sample of 260 college alumni, 117 favor keeping the coach. Test at the .01 level of significance whether the proportion of alumni who support the coach is less than 50 percent.

Explanation / Answer

a) H0: 0.5

H1: < 0.5

b) Reject H0 if z is < -2.33

c)

here std error =((1-)/n)1/2 =0.031

sample proportion hat =117/260 =0.45

hence test statistic z =(hat-)/std error =(0.45-0.5)/0.031 =-1.612

d)

do not reject H0. There is insufficient evidence to conclude the population proportion
of alumni supporting the coach is less than .50.

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