Question

After a losing season, there is a great uproar to fire the head football coach. In a random sample of 320 college alumni, 144 favor keeping the coach. Test at the .02 significance level whether the proportion of alumni who support the coach is less than 50 percent.

a. state the null and alternate hypothesis, round 2 decimals:

H0: pi is greater than or equall to __

Hi:Pi is less than ____

b. state the decision rule for .02 significance level, round 2 decimals.

reject H0: if z is < ____

c. compute the value of the test statistic rounded to 3 decimals

d. test at the .02 level of sig 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

Answer 1

Solution :

a. Given the claim is , test whether the proportion of alumni who support the coach is less than 50 percent,

Vs

b. Given that level of significance alpha = 0.02

We will use standard normal table ,and for this left tailed test we get critical value zc = -2.05

So the decision rule is :Reject Ho ,if test statitstics z is < -2.05 , otherwise fail to reject Ho.

c. To find test statistics.

Given that ,population proportion pi = 0.5 ,sample proportion p = x/n = 144/320 = 0.45

z = -1.789

d. Decision: As here test statistics -1.789 < critcal value -2.05 , we reject Ho.

There is sufficient evidence to conclude that the population proportion is less than 50 percent.