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 200 college alumni, 74 favor keeping the coach. Test at the 0.01 level of significance whether the proportion of alumni who support the coach is less than 50%.

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.)

State the decision rule for 0.01 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 0.01 level of significance whether the proportion of alumni who support the coach is less than 50%.

Reject or do not reject???? H0. There is insufficient or sufficient???? evidence to conclude the population proportion
of alumni supporting the coach is less than 0.50.

After a losing season, there is a great uproar to fire the head football coach. In a random sample of 200 college alumni, 74 favor keeping the coach. Test at the 0.01 level of significance whether the proportion of alumni who support the coach is less than 50%.

Explanation / Answer

Answer:

a) Null Hypothesis (Ho): ? ? 0.50

Alternative Hypothesis (Ha): ? < 0.50

b) Using Z-tables, the critical value is

Z (0.01) = -2.33

Reject H0 if z is < -2.33

c) Sample proportion, p = X/n = 74/200 = 0.37

Test Statistics

Z = (p

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