Null-hypothesis for a Single Sample Z-test for

ProportionsConceptual 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 Single-Sample Z-test for proportions makes it possible to statistically compare a population proportion with a 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 between the population proportion and the sample proportion.

Example 1

A guest on a local radio station claims that 10% of Dallas citizens commute to work. A survey on commuting by car was done on a random sample of 1000 citizens, and found car commuting to be 12%. Test an appropriate hypothesis and state your conclusion.

Template for a Single-Sample Z-test Null-Hypothesis

A guest on a local radio station claims that 10% of Dallas citizens commute to work. A survey on commuting by car was done on a random sample of 1000 citizens, and found car commuting to be 12%. Test an appropriate hypothesis and state your conclusion.

There is no statistically significant difference between the population proportion and the sample proportion.

A guest on a local radio station claims that 10% of Dallas citizens commute to work. A survey on commuting by car was done on a random sample of 1000 citizens, and found car commuting to be 12%. Test an appropriate hypothesis and state your conclusion.

There is no statistically significant difference between the population proportion and the sample proportion.

Null-hypothesis for this Problem

A guest on a local radio station claims that 10% of Dallas citizens commute to work. A survey on commuting by car was done on a random sample of 1000 citizens, and found car commuting to be 12%. Test an appropriate hypothesis and state your conclusion.

There is no statistically significant difference between the population proportion and the sample proportion.

There is no statistically significant difference between the population proportion of Dallas citizens who commute to work and a random sample of 1000 citizens who indicated on a survey that they commute to work.

A guest on a local radio station claims that 10% of Dallas citizens commute to work. A survey on commuting by car was done on a random sample of 1000 citizens, and found car commuting to be 12%. Test an appropriate hypothesis and state your conclusion.

There is no statistically significant difference between the population proportion and the sample proportion.

There is no statistically significant difference between the population proportion of Dallas citizens who commute to work and a random sample of 1000 citizens who indicated on a survey that they commute to work.

A guest on a local radio station claims that 10% of Dallas citizens commute to work. A survey on commuting by car was done on a random sample of 1000 citizens, and found car commuting to be 12%. Test an appropriate hypothesis and state your conclusion.

There is no statistically significant difference between the population proportion and the sample proportion.

There is no statistically significant difference between the population proportion of Dallas citizens who commute to work and a random sample of 1000 citizens who indicated on a survey that they commute to work.

A guest on a local radio station claims that 10% of Dallas citizens commute to work. A survey on commuting by car was done on a random sample of 1000 citizens, and found car commuting to be 12%. Test an appropriate hypothesis and state your conclusion.

Example 2

A state university wants to increase its retention rate of 4% for graduating students from the previous year. After implementing several new programs during the last two years, the university reevaluated its retention rate using a random sample of 352 students and found the retention rate at 5%. Test an appropriate hypothesis and state your conclusion.

A state university wants to increase its retention rate of 4% for graduating students from the previous year. After implementing several new programs during the last two years, the university reevaluated its retention rate using a random sample of 352 students and found the retention rate at 5%. Test an appropriate hypothesis and state your conclusion.

Template for a Single-Sample Z-test Null-Hypothesis

A state university wants to increase its retention rate of 4% for graduating students from the previous year. After implementing several new programs during the last two years, the university reevaluated its retention rate using a random sample of 352 students and found the retention rate at 5%. Test an appropriate hypothesis and state your conclusion.

There is no statistically significant difference between the population proportion and the sample proportion.

A state university wants to increase its retention rate of 4% for graduating students from the previous year. After implementing several new programs during the last two years, the university reevaluated its retention rate using a random sample of 352 students and found the retention rate at 5%. Test an appropriate hypothesis and state your conclusion.

There is no statistically significant difference between the population proportion and the sample proportion.

Null-hypothesis for this Problem

A state university wants to increase its retention rate of 4% for graduating students from the previous year. After implementing several new programs during the last two years, the university reevaluated its retention rate using a random sample of 352 students and found the retention rate at 5%. Test an appropriate hypothesis and state your conclusion.

There is no statistically significant difference between the population proportion and the sample proportion.

There is no statistically significant difference between the 4% goal in retention rate increase from the previous year and a 5% increase in retention rate found in a random sample of 352 students in the current year.

A state university wants to increase its retention rate of 4% for graduating students from the previous year. After implementing several new programs during the last two years, the university reevaluated its retention rate using a random sample of 352 students and found the retention rate at 5%. Test an appropriate hypothesis and state your conclusion.

There is no statistically significant difference between the population proportion and the sample proportion.

There is no statistically significant difference between the 4% goal in retention rate increase from the previous year and a 5% increase in retention rate found in a random sample of 352 students in the current year.

A state university wants to increase its retention rate of 4% for graduating students from the previous year. After implementing several new programs during the last two years, the university reevaluated its retention rate using a random sample of 352 students and found the retention rate at 5%. Test an appropriate hypothesis and state your conclusion.

There is no statistically significant difference between the population proportion and the sample proportion.

There is no statistically significant difference between the 4% goal in retention rate increase from the previous year and a 5% increase in retention rate found in a random sample of 352 students in the current year.