Question

A report by the NCAA states that 57.6% of football injuries occur during practices. A trainer for a particular team claims that there are significantly less practice injuries in his team’s conference, so he randomly selects 36 reported injuries and finds that 17 occurred during practice. Conduct a hypothesis test to evaluate this claim at the .05 significance level. Be sure to include the following:

a) The null and alternative hypotheses.

b) The value of the point estimator for the parameter being tested.

c) The value of the test statistic.

d) The p-value.

e) A decision as to whether or not the null hypothesis should be rejected.

f) An interpretation of the outcome of the test in terms of the trainer’s claim.

Answer 1

Solution :

a ) This is the Left tailed test .

The null and alternative hypothesis is

H0 : p = 0.576

Ha : p < 0.576

b ) n = 36

x = 17

= x / n = 17 / 36 = 0.47

P0 = 0.576

1 - P0 = 1 - 0.576 =0.424

c ) Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

=0.47-0.576 / [(0.576*0.424) / 36]

= -1.29

Test statistic = z = -1.29

d ) P(z < -1.29 ) = 0.0985

P-value =  0.0985

= 0.05

P-value >

0.0985 > 0.05

d ) Fail to reject the null hypothesis .

e ) There is not sufficient evidence to suggest that