Homework SourseMimi was the 5th seed in 2014 UMUC Tennis Open that took pla
Mimi was the 5th seed in 2014 UMUC Tennis Open that took place in August. In this tournament, she won 75 of her 100 serving games. Based on UMUC Sports Network, she wins 80% of the serving games in her 5-year tennis career.
(a) (3 pts) Find a 90% confidence interval estimate of the proportion of serving games Mimi won. (Show work and round the answer to three decimal places)
(b) (1 pts) Based on the confidence interval estimate you got in part (a), is this tournament result consistent with her career record of 80%? Why or why not? Please explain your conclusion.
Solution
a) 90% confidence interval estimate of the proportion of serving games Mimi won = (0.679,0.821)
b) this tournament result is consistent with her career record of 80% because 0.80 is included in the above 90% confidence interval
| sample size n | 100 |
| Sample x | 75 |
| Sample proportion phat= | 0.75 |
| Confidence coefficent, 1-alpha= | 90% |
| alpha= | 10% |
| Zalpha/2=(z s.t P( Z> z)=alpha/2= | 1.644854 |
| SD(p)=sqrt(phat*(1-phat)/n) | 0.043301 |
| Upper limit=phat+Zalpha/2*SD(p) | 0.821224 |
| Lower limit=phat+Zalpha/2*SD(p)= | 0.678776 |
