Question

The coach of a very popular men’s basketball team claims that the average distance the fans travel to the campus to watch a game is 35 miles. The team members feel otherwise. A sample of 16 fans who travel to games was randomly selected and yielded a mean of M= 36 miles and s= 5 miles. Test the coach’s claim at the 5% (.05) level of significance.

one-tailed or two-tailed test:

State the hypotheses:

df=

tα or t value for the critical region =

s_M =   

t (test statistic)=

Decision:

Answer 1

Solution:

Given:

Claim: the average distance the fans travel to the campus to watch a game is 35 miles.

that is miles

Sample size = n = 16

Sample mean = miles

Sample standard deviation = s= 5 miles.

level of significance = 0.05

Part i) one-tailed or two-tailed test:

Since claim is non-directional, this is two tailed test.

Part ii) State the hypotheses:

Vs

Part iii) df=.........?

df= n - 1 = 16 -1 = 15

Part iv) tα or t value for the critical region =......?

Two tail area = level of significance = 0.05 and df = 15

t_α = t_0.05 = 2.131

Since this is two tailed test, t critical values areL ( -2.131 , 2.131 )

Part v) s_M =.........?

Part vi) t (test statistic)=...........?

Part vii) Decision:

Decision Rule:

Reject null hypothesis H0, if absolute t test statistic value > t critical value =2.131, otherwise we fail to reject H0

Since absolute t test statistic value = <   t critical value =2.131,  we fail to reject H0