null hypothesis for a two sample z test

Null-hypothesis for a Two-Sample Z-test for Proportions

Conceptual Explanation

With hypothesis testing we are setting up a null-hypothesis

With hypothesis testing we are setting up a null-hypothesis – the probability that there is no effect or relationship

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.

As you may recall, a Two-Sample Z-test for proportions makes it possible to statistically compare one sample proportion with another sample proportion.

Here is a template for writing a null-hypothesis for a single-sample Z-test:

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.

Example 1

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.

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.

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.

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.

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.

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.

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.

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.

Example 2

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?

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?

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.

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.

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.

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.

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.