Which of the following should be done to test a hypothesis that two population proportion are the same?
A hypothesis test can help determine if a difference in the estimated proportions reflects a difference in the population proportions. The difference of two proportions follows an approximate normal distribution. Generally, the null hypothesis states that the two proportions are the same. That is, H 0: p A = p B.
What is a 2 Prop z-test for?
The Two-Sample Z-test is used to compare the means of two samples to see if it is feasible that they come from the same population. The null hypothesis is: the population means are equal.
How do you find the p-value for two proportion z test?
Since we have a two-tailed test, the P-value is the probability that the z-score is less than -2.13 or greater than 2.13. We use the Normal Distribution Calculator to find P(z < -2.13) = 0.017, and P(z > 2.13) = 0.017. Thus, the P-value = 0.017 + 0.017 = 0.034.
How to estimate the proportions of two populations?
Since we don’t know the (assumed) common population proportion p any more than we know the proportions p 1 and p 2 of each population, we can estimate p using: the proportion of “successes” in the two samples combined. And, hence, our test statistic becomes:
Which is an example of a finite population?
When we have smaller, finite populations, however, such as the students in a high school or the residents of a small town, the formula we derived previously requires a slight modification. Let’s start, as usual, by taking a look at an example. A researcher is studying the population of a small town in India of N = 2000 people.
When to use a sample proportion of 0.50?
Because the researcher has many different questions on the survey, it would behoove her to use a sample proportion of 0.50 in her calculations. If the maximum error ϵ is 0.04, the sample proportion is 0.5, and the researcher doesn’t make the finite population correction, then she needs:
Which is the correct statistic to test the null hypothesis?
If p 1 = the proportion of the non-smoker population who reply “yes” and p 2 = the proportion of the smoker population who reply “yes,” then we are interested in testing the null hypothesis: against the alternative hypothesis: Before we can actually conduct the hypothesis test, we’ll have to derive the appropriate test statistic.