2-Sample ZTest
2-Sample Ttest
Dependent samples
2Prop Z-test
Conditions
100
These are the null and alternative hypotheses to test the claim that males perform better in math than females using um and uf
What is
Ho: um ≤ uf
Ha: um >uf
100
This is the critical value for Ha: u1<u2, alpha=.10, n1=11 and n2=14 and population variances are equal
What is df = 24
100
Classify the two samples as dependent or independent:
The SAT scores of 25 males and the SAT scores of 25 females.
What are independent samples
100
Find the pooled proportion
Claim: p1<p2; alpha=0.05, x1=27, n1=65, x2=31, n2=63
p=58/128=0.453
100
These are the conditions for a 2 sample z-test
What are both samples are randomly selected and independent, both populations are normal or both samples are >30
200
Find the critical value(s) for a 2-tailed 2-sample z-test if alpha=0.05
What is Zc=-1.96, 1.96
200
This is the critical value for Ha: u1<u2, alpha=.10, n1=11 and n2=14 and population variances are not equal
What is df = 10
200
Classify the samples as dependent or independent:
SAT scores of 25 males and SAT scores of the same 25 males after participation in a review course.
What are dependent Samples
200
Verify whether the conditions for inference are satisfied by finding p-bar, then using it to find n1p, n1q, n2p and n2q
Claim: p1<p2; alpha=0.05, x1=27, n1=65, x2=31, n2=63
n1p, n1q, n2p and n2q are all >5
29.5,35.5,28.5,34.5
200
These are the conditions for a 2 sample t-test
Both samples are randomly selected and independent, population standard deviations are unknown, one or both samples are less than 30 and both populations are normal.
300
This is the test statistic for the claim u1=u2 given sample statistics: x̄1=16, s1=1.1, n1=50, x̄2=14, s2=1.5, n2=50,
z=7.6 and p=2.92x10-14
300
This is the standardized test statistic and p-value for the claim Ha: u1<u2, alpha=.10, x̄1=36, s1=2.3 n1=11 x̄2=39, s2=2.1 and n2=14 and population variances are equal
What is z=-3.40 and P=.001
300
six employees process daily orders with and without music playing in the background. Does music increase the number of orders processed? Find the critical region using alpha=.01
No Music Music
60 64
48 49
53 57
51 53
49 48
62 66
t<-3.36
300
Find the rejection region for the 2 proportion z test:
Claim: p1<p2; alpha=0.05, x1=27, n1=65, x2=31, n2=63, alpha = 0.05
What is z<-1.96 and z>1.96
300
What are the conditions for a paired sample t-test?
What are both samples are randomly selected and dependent, either both sample sizes are >30 or both populations are normally distributed if either sample is <30
400
This is the decision about H0 for the claim u1=u2 given sample statistics: x̄1=16, s1=1.1, n1=50, x̄2=14, s2=1.5, n2=50,
What is reject Ho
400
0This is the decision and conclusion for the claim Ha: u1<u2, alpha=.10, x̄1=36, s1=2.3 n1=11 x̄2=39, s2=2.1 and n2=14 and population variances are equal
Decision: Reject H0
Conclusion: There is sufficient evidence to support the claim that u1<u2
400
six employees process daily orders with and without music playing in the background. Does music increase the number of orders processed? Find the test statistic and p-value using alpha =0.01
No Music Music
60 64
48 49
53 57
51 53
49 48
62 66
t=-2.77 p=.02
400
Find the test statistic and p-value for the 2 proportion z test:
Claim: p1<p2; alpha=0.05, x1=27, n1=65, x2=31, n2=63, alpha = 0.05
z= -0.87
p=.192
400
What are the conditions for a 2-Proportion z-test?
Both samples are random and independent. all nps and nqs are >5
500
This is the conclusion for the claim u1=u2 given sample statistics: x̄1=16, s1=1.1, n1=50, x̄2=14, s2=1.5, n2=50,
What is "there is sufficient evidence to reject the claim that u1=u2
500
35 residents of PSL have mean salary $54,000 with standard deviation of $4000. 32 Vero residents have mean salary 61,000 with standard deviation of $4400. Is there enough evidence that Vero salaries are higher? Assume variances are equal. Find the test statistic, p-value and conclusion
t=-6.82, p=.00000000179
There is enough evidence to support the claim that Vero salaries are higher than PSL salaries
500
six employees process daily orders with and without music playing in the background. Does music increase the number of orders processed? Find the decision and conclusion using alpha=0.01
No Music Music
60 64
48 49
53 57
51 53
49 48
62 66
Decision: Fail to reject Ho
Conclusion: at the 1% level of significance, There is not enough evidence to support the claim that adding music increases the number of orders produced by the employees.
500
Find the decision and conclusion for the 2 proportion z test:
Claim: p1<p2; alpha=0.05, x1=27, n1=65, x2=31, n2=63, alpha = 0.05
Fail to reject Ho
There is not sufficient evidence to support the claim that p1<p2
500
Verify whether the conditions for inference are justified. Show all calculations
17 out of 40 males and 5 out of 30 females owns a truck. Is there enough evidence that the proportion of males who own a truck is higher than that of females?
p-bar=(17+5)/(40+30)=22/70=.3143
n1p=12.6, n1q=27.4, n2p=9.4, n2q=20.6.
Since all are >5, conditions are justified