In: Math
1/12/2018 Section 9.1 Homework-Rachel Yehnert
2. Since an instant replay system for tennis was introduced at a major tournament, men challenged 1391 referee calls, with the result that 423 of the calls were overturned. Women challenged 765 referee calls, and 227 of the calls were overturned. Use a 0.01 significance level to test the claim that men and women have equal success in challenging calls. Complete parts (a) through (c) below.
a. Test the claim using a hypothesis test.
Consider the first sample to be the sample of male tennis players who challenged referee calls and the second sample to be the sample of female tennis players who challenged referee calls. What are the null and alternative hypotheses for the hypothesis test?
A. H0:p1≥p2 H1: p1 ≠p2 D. H0:p1=p2 H1: p1 >p2
Identify the test statistic.
B. H0:p1=p2 H1: p1 <p2 E. H0:p1≤p2 H1: p1 ≠p2
C. H0 : p1 = p2 H1: p1 ≠p2 F. H0:p1≠p2 H1: p1 =p2
z= 0.36
(Round to two decimal places as needed.)
Identify the Pvalue.
Pvalue = 0.721
(Round to three decimal places as needed.)
What is the conclusion based on the hypothesis test?
The Pvalue is greater than the significance level of = 0.01,
so
is not sufficient evidence to warrant rejection of the claim that
women and men have equal success in challenging calls.
b. Test the claim by constructing an
appropriate confidence interval.
The 99% confidence interval is − 0.046 < p1 − p2 < 0.060
.
(Round to three decimal places as needed.)
What is the conclusion based on the confidence interval?
Because the confidence interval limits include 0, there does not appear to be a significant difference between the
two proportions. There is not sufficient evidence to warrant rejection of the claim that men and women have equal success in challenging calls.
c. Based on the results, does it appear that men and women have equal success in challenging calls?
It does not appear that men and women have equal success in challenging calls. Women have more
success.
It appears that men and women have equal success in challenging calls.
It does not appear that men and women have equal success in challenging calls. Men have more success.
The results are inconclusive.
How do you find each answer and how do you input it into stat crunch to get the answer
For men, we have that the sample size is N1=1391, the number of favorable cases is X1=423, so then the sample proportion is p^1=X1/N1=423/1391=0.3041
For women, we have that the sample size is N2=765, the number of favorable cases is X2=227, so then the sample proportion is p^2=X2/N2=227/765=0.2967
The value of the pooled proportion is computed as p¯=X1+X2/N1+N2 =423+227/1391+765 =0.3015
Also, the given significance level is α=0.01.
(1) Null and Alternative Hypotheses
The following null and alternative hypotheses need to be tested:
Ho:p1=p2
Ha:p1≠p2
This corresponds to a two-tailed test, for which a z-test for two population proportions needs to be conducted.
(2) Rejection Region
Based on the information provided, the significance level is α=0.01, and the critical value for a two-tailed test is zc=2.58.
The rejection region for this two-tailed test is R = \{z: |z| > 2.58\}R={z:∣z∣>2.58}
(3) Test Statistics
The z-statistic is computed as follows:
z=p^1−p^2/(p¯(1−p¯)(1/n1+1/n2)) =0.3041−0.2967/(0.3015⋅(1−0.3015)(1/1391+1/765))
z=0.36
(4) Decision about the null hypothesis
Since it is observed that ∣z∣=0.367≤zc=2.58, it is then concluded that the null hypothesis is not rejected.
Using the P-value approach: The p-value is p = 0.721, and since p=0.7214≥0.01, it is concluded that the null hypothesis is not rejected.
(5) Conclusion
It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population proportion p1 is different than p2, at the 0.01 significance level.It appears that men and women have equal success in challenging calls.