Mimi was the 5th seed in 2014 UMUC Tennis Open that took place in August. In thi
ID: 3152543 • Letter: M
Question
Mimi was the 5th seed in 2014 UMUC Tennis Open that took place in August. In this tournament, she won 80 of her 100 serving games. Based on UMUC Sports Network, she wins 75% of the serving games in her 5-year tennis career. In order to determine if this tournament result is better than her career record of 75%. We would like to perform the following hypothesis test: Ho: p = 0.75 Ha: p >0.75 (a) Find the test statistic. (Show work and round the answer to two decimal places) (b) Determine the P-value for this test. (Show work and round the answer to three decimal places) (c) Is there sufficient evidence to justify the rejection of Ho at the alpha = 0.02 level? Explain.
Explanation / Answer
Here we have to test the hypothesis that,
H0 : p = 0.75 Vs Ha: p >0.75
where p is population proportion.
Assume alpha = level of significance = 0.02
Given that, x = number of games she won = 80
n = number of serving games = 100
The test statistic is,
Z = (p^ - p) / sqrt ( (p*q)/n )
p^ is sample proportion.
p^ = x/n = 80 / 100 = 0.8
p = 0.75
q = 1 - p = 1 - 0.75 = 0.25
sqrt ( (p*q) / n) = sqrt ( (0.75*0.25) / 100 ) = sqrt(0.001875) = 0.0433
Z = (0.8 - 0.75) / 0.0433 = 0.05 / 0.0433 = 1.15
P-value we can find by using EXCEL.
syntax is,
=1 - NORMSDIST(z)
where z is test statistic value.
P-value = 0.124
P-value > alpha
Accept H0 at 2% level of significance.
Conclusion : There is sufficient evidence to say that she wins her career record of 75%.