Question

The percentage of complete passes is an important measure for a quarterback in the NFL. A particular quarterback has a career completion percentage of 55%. The quarterback got a new coach and then played a few games where he completed 48 of 100 passes.

a. Specify the null and alternative hypotheses to determine whether the proportion of completed passes has decreased with the new coach.

b. Calculate the value of the test statistic and the p-value.

c. At the 5% significance level, can you conclude that the quarterback’s completion percentage has decreased?

Answer 1

Answer:

Here given

n=100

x= 48

 = 0.55

We have to test

 Vs $H_1:p<0.55$

p^ = x/n

= 48/100

= 0.48

Value of test statistic

=(0.48-0.55)/ sqrt(0.55*0.45/100)

= -1.407053

p-value = p[z <-1.407053]

=0.07970584

Decision: Here p-value = 0.07970584 > 0.05 therefore we failed to reject H0 at 5% l.o.s.

Conclusion: we  do not reject the null hypothesis so we failed to conclude that quarterback's completion percentage has decreased.