null hypothesis for a two sample z test
DESCRIPTION
Null hypothesis for a Two Sample Z TestTRANSCRIPT
![Page 1: Null hypothesis for a Two Sample Z Test](https://reader035.vdocuments.mx/reader035/viewer/2022062220/55847979d8b42abf538b51c1/html5/thumbnails/1.jpg)
Null-hypothesis for a Two-Sample Z-test for Proportions
Conceptual Explanation
![Page 2: Null hypothesis for a Two Sample Z Test](https://reader035.vdocuments.mx/reader035/viewer/2022062220/55847979d8b42abf538b51c1/html5/thumbnails/2.jpg)
With hypothesis testing we are setting up a null-hypothesis
![Page 3: Null hypothesis for a Two Sample Z Test](https://reader035.vdocuments.mx/reader035/viewer/2022062220/55847979d8b42abf538b51c1/html5/thumbnails/3.jpg)
With hypothesis testing we are setting up a null-hypothesis – the probability that there is no effect or relationship
![Page 4: Null hypothesis for a Two Sample Z Test](https://reader035.vdocuments.mx/reader035/viewer/2022062220/55847979d8b42abf538b51c1/html5/thumbnails/4.jpg)
With hypothesis testing we are setting up a null-hypothesis – the probability that there is no effect or relationship – and then we collect evidence that leads us to either accept or reject that null hypothesis.
![Page 5: Null hypothesis for a Two Sample Z Test](https://reader035.vdocuments.mx/reader035/viewer/2022062220/55847979d8b42abf538b51c1/html5/thumbnails/5.jpg)
As you may recall, a Two-Sample Z-test for proportions makes it possible to statistically compare one sample proportion with another sample proportion.
![Page 6: Null hypothesis for a Two Sample Z Test](https://reader035.vdocuments.mx/reader035/viewer/2022062220/55847979d8b42abf538b51c1/html5/thumbnails/6.jpg)
Here is a template for writing a null-hypothesis for a single-sample Z-test:
![Page 7: Null hypothesis for a Two Sample Z Test](https://reader035.vdocuments.mx/reader035/viewer/2022062220/55847979d8b42abf538b51c1/html5/thumbnails/7.jpg)
Here is a template for writing a null-hypothesis for a single-sample Z-test:
There IS NO statistically significant difference in the proportion of the _________ group results and the _______ group results.
![Page 8: Null hypothesis for a Two Sample Z Test](https://reader035.vdocuments.mx/reader035/viewer/2022062220/55847979d8b42abf538b51c1/html5/thumbnails/8.jpg)
Example 1
![Page 9: Null hypothesis for a Two Sample Z Test](https://reader035.vdocuments.mx/reader035/viewer/2022062220/55847979d8b42abf538b51c1/html5/thumbnails/9.jpg)
A swimming school wants to determine whether a recently hired instructor is working out. Sixteen out of 25 of Instructor A's students passed the lifeguard certification test on the first try. In comparison, 57 out of 72 of more experienced Instructor B's students passed the test on the first try. Is Instructor A's success rate worse than Instructor B's? Use α = 0.05.
![Page 10: Null hypothesis for a Two Sample Z Test](https://reader035.vdocuments.mx/reader035/viewer/2022062220/55847979d8b42abf538b51c1/html5/thumbnails/10.jpg)
Here’s the Problem AgainA swimming school wants to determine whether a recently hired instructor is working out. Sixteen out of 25 of Instructor A's students passed the lifeguard certification test on the first try. In comparison, 57 out of 72 of more experienced Instructor B's students passed the test on the first try. Is Instructor A's success rate worse than Instructor B's? Use α = 0.05.
![Page 11: Null hypothesis for a Two Sample Z Test](https://reader035.vdocuments.mx/reader035/viewer/2022062220/55847979d8b42abf538b51c1/html5/thumbnails/11.jpg)
ProblemA swimming school wants to determine whether a recently hired instructor is working out. Sixteen out of 25 of Instructor A's students passed the lifeguard certification test on the first try. In comparison, 57 out of 72 of more experienced Instructor B's students passed the test on the first try. Is Instructor A's success rate worse than Instructor B's? Use α = 0.05.
Template for Null-hypothesis for Two-Sample Z-TestThere IS NO statistically significant difference in the proportion of the first group’s results and the second group’s results.
![Page 12: Null hypothesis for a Two Sample Z Test](https://reader035.vdocuments.mx/reader035/viewer/2022062220/55847979d8b42abf538b51c1/html5/thumbnails/12.jpg)
ProblemA swimming school wants to determine whether a recently hired instructor is working out. Sixteen out of 25 of Instructor A's students passed the lifeguard certification test on the first try. In comparison, 57 out of 72 of more experienced Instructor B's students passed the test on the first try. Is Instructor A's success rate worse than Instructor B's? Use α = 0.05.
Template for Null-hypothesis for Two-Sample Z-TestThere IS NO statistically significant difference in the proportion of the first group’s results and the second group’s results.
![Page 13: Null hypothesis for a Two Sample Z Test](https://reader035.vdocuments.mx/reader035/viewer/2022062220/55847979d8b42abf538b51c1/html5/thumbnails/13.jpg)
ProblemA swimming school wants to determine whether a recently hired instructor is working out. Sixteen out of 25 of Instructor A's students passed the lifeguard certification test on the first try. In comparison, 57 out of 72 of more experienced Instructor B's students passed the test on the first try. Is Instructor A's success rate worse than Instructor B's? Use α = 0.05.
Template for Null-hypothesis for Two-Sample Z-TestThere IS NO statistically significant difference in the proportion of the first group’s results and the second group’s results.
Null-hypothesis There IS NO statistically significant difference in the proportion of instructor A’s students and the proportion of instructor B’s students who passed their lifeguard certification test.
![Page 14: Null hypothesis for a Two Sample Z Test](https://reader035.vdocuments.mx/reader035/viewer/2022062220/55847979d8b42abf538b51c1/html5/thumbnails/14.jpg)
ProblemA swimming school wants to determine whether a recently hired instructor is working out. Sixteen out of 25 of Instructor A's students passed the lifeguard certification test on the first try. In comparison, 57 out of 72 of more experienced Instructor B's students passed the test on the first try. Is Instructor A's success rate worse than Instructor B's? Use α = 0.05.
Template for Null-hypothesis for Two-Sample Z-TestThere IS NO statistically significant difference in the proportion of the first group’s results and the second group’s results.
Null-hypothesis There IS NO statistically significant difference in the proportion of instructor A’s students and the proportion of instructor B’s students who passed their lifeguard certification test.
![Page 15: Null hypothesis for a Two Sample Z Test](https://reader035.vdocuments.mx/reader035/viewer/2022062220/55847979d8b42abf538b51c1/html5/thumbnails/15.jpg)
ProblemA swimming school wants to determine whether a recently hired instructor is working out. Sixteen out of 25 of Instructor A's students passed the lifeguard certification test on the first try. In comparison, 57 out of 72 of more experienced Instructor B's students passed the test on the first try. Is Instructor A's success rate worse than Instructor B's? Use α = 0.05.
Template for Null-hypothesis for Two-Sample Z-TestThere IS NO statistically significant difference in the proportion of the first group’s results and the second group’s results.
Null-hypothesis There IS NO statistically significant difference in the proportion of instructor A’s students and the proportion of instructor B’s students who passed their lifeguard certification test.
![Page 16: Null hypothesis for a Two Sample Z Test](https://reader035.vdocuments.mx/reader035/viewer/2022062220/55847979d8b42abf538b51c1/html5/thumbnails/16.jpg)
ProblemA swimming school wants to determine whether a recently hired instructor is working out. Sixteen out of 25 of Instructor A's students passed the lifeguard certification test on the first try. In comparison, 57 out of 72 of more experienced Instructor B's students passed the test on the first try. Is Instructor A's success rate worse than Instructor B's? Use α = 0.05.
Template for Null-hypothesis for Two-Sample Z-TestThere IS NO statistically significant difference in the proportion of the first group’s results and the second group’s results.
Null-hypothesis There IS NO statistically significant difference in the proportion of instructor A’s students and the proportion of instructor B’s students who passed their lifeguard certification test.
![Page 17: Null hypothesis for a Two Sample Z Test](https://reader035.vdocuments.mx/reader035/viewer/2022062220/55847979d8b42abf538b51c1/html5/thumbnails/17.jpg)
Example 2
![Page 18: Null hypothesis for a Two Sample Z Test](https://reader035.vdocuments.mx/reader035/viewer/2022062220/55847979d8b42abf538b51c1/html5/thumbnails/18.jpg)
In a small town in Massachusetts, a town well supplied water that was contaminated by industrial chemicals to the west side residents but not to the east side residents, because they used a different well. During that period of time a sample of 414 births on the west side showed 16 birth defects and a sample of 228 births on the east side showed 3 birth defects. A law suit is pending against the city for negligence. How strong is their evidence statistically?
![Page 19: Null hypothesis for a Two Sample Z Test](https://reader035.vdocuments.mx/reader035/viewer/2022062220/55847979d8b42abf538b51c1/html5/thumbnails/19.jpg)
Here’s the problem againIn a small town in Massachusetts, a town well supplied water that was contaminated by industrial chemicals to the west side residents but not to the east side residents, because they used a different well. During that period of time a sample of 414 births on the west side showed 16 birth defects and a sample of 228 births on the east side showed 3 birth defects. A law suit is pending against the city for negligence. How strong is their evidence statistically?
![Page 20: Null hypothesis for a Two Sample Z Test](https://reader035.vdocuments.mx/reader035/viewer/2022062220/55847979d8b42abf538b51c1/html5/thumbnails/20.jpg)
ProblemIn a small town in Massachusetts, a town well supplied water that was contaminated by industrial chemicals to the west side residents but not to the east side residents, because they used a different well. During that period of time a sample of 414 births on the west side showed 16 birth defects and a sample of 228 births on the east side showed 3 birth defects. A law suit is pending against the city for negligence. How strong is their evidence statistically?
Template for Null-hypothesis for Two-Sample Z-TestThere IS NO statistically significant difference in the proportion of the first group’s results and the second group’s results.
![Page 21: Null hypothesis for a Two Sample Z Test](https://reader035.vdocuments.mx/reader035/viewer/2022062220/55847979d8b42abf538b51c1/html5/thumbnails/21.jpg)
ProblemIn a small town in Massachusetts, a town well supplied water that was contaminated by industrial chemicals to the west side residents but not to the east side residents, because they used a different well. During that period of time a sample of 414 births on the west side showed 16 birth defects and a sample of 228 births on the east side showed 3 birth defects. A law suit is pending against the city for negligence. How strong is their evidence statistically?
Template for Null-hypothesis for Two-Sample Z-TestThere IS NO statistically significant difference in the proportion of the first group’s results and the second group’s results.
Null-hypothesis There IS NO statistically significant difference in the proportion of birth defects between west side residents and east side residents.
![Page 22: Null hypothesis for a Two Sample Z Test](https://reader035.vdocuments.mx/reader035/viewer/2022062220/55847979d8b42abf538b51c1/html5/thumbnails/22.jpg)
ProblemIn a small town in Massachusetts, a town well supplied water that was contaminated by industrial chemicals to the west side residents but not to the east side residents, because they used a different well. During that period of time a sample of 414 births on the west side showed 16 birth defects and a sample of 228 births on the east side showed 3 birth defects. A law suit is pending against the city for negligence. How strong is their evidence statistically?
Template for Null-hypothesis for Two-Sample Z-TestThere IS NO statistically significant difference in the proportion of the first group’s results and the second group’s results.
Null-hypothesis There IS NO statistically significant difference in the proportion of birth defects between west side residents and east side residents.
![Page 23: Null hypothesis for a Two Sample Z Test](https://reader035.vdocuments.mx/reader035/viewer/2022062220/55847979d8b42abf538b51c1/html5/thumbnails/23.jpg)
ProblemIn a small town in Massachusetts, a town well supplied water that was contaminated by industrial chemicals to the west side residents but not to the east side residents, because they used a different well. During that period of time a sample of 414 births on the west side showed 16 birth defects and a sample of 228 births on the east side showed 3 birth defects. A law suit is pending against the city for negligence. How strong is their evidence statistically?
Template for Null-hypothesis for Two-Sample Z-TestThere IS NO statistically significant difference in the proportion of the first group’s results and the second group’s results.
Null-hypothesis There IS NO statistically significant difference in the proportion of birth defects between west side residents and east side residents.
![Page 24: Null hypothesis for a Two Sample Z Test](https://reader035.vdocuments.mx/reader035/viewer/2022062220/55847979d8b42abf538b51c1/html5/thumbnails/24.jpg)
ProblemIn a small town in Massachusetts, a town well supplied water that was contaminated by industrial chemicals to the west side residents but not to the east side residents, because they used a different well. During that period of time a sample of 414 births on the west side showed 16 birth defects and a sample of 228 births on the east side showed 3 birth defects. A law suit is pending against the city for negligence. How strong is their evidence statistically?
Template for Null-hypothesis for Two-Sample Z-TestThere IS NO statistically significant difference in the proportion of the first group’s results and the second group’s results.
Null-hypothesis There IS NO statistically significant difference in the proportion of birth defects between west side residents and east side residents.