How do you find the test statistic for a population proportion?
The basic procedure is:
- State the null hypothesis H0 and the alternative hypothesis HA.
- Set the level of significance .
- Calculate the test statistic: z = p ^ − p o p 0 ( 1 − p 0 ) n.
- Calculate the p-value.
- Make a decision. Check whether to reject the null hypothesis by comparing p-value to .
How do you find the population proportion?
Formula Review p′ = x / n where x represents the number of successes and n represents the sample size. The variable p′ is the sample proportion and serves as the point estimate for the true population proportion.
How to do a hypothesis test for a population proportion?
A Hypothesis Test for a Population Proportion 1. Intro 3. Using Confidence Intervals to Test Hypotheses Our main goal is in finding the probability of a difference between a sample mean p̂ and the claimed value of the population proportion, p0.
What is the formula for the sample proportion statistic?
Recall from Linking Probability to Statistical Inference that the formula for the z -score of a sample proportion is as follows: For this example, we calculate: This z -score is called the test statistic. It tells us the sample proportion of 0.83 is about 2.12 standard errors above the population proportion given in the null hypothesis.
How to calculate the population mean and proportion?
Calculate the sample size required to estimate a population mean and a population proportion given a desired confidence level and margin of error During an election year, we see articles in the newspaper that state confidence intervals in terms of proportions or percentages.
How to find the true proportion of Statistics students?
Use the “plus-four” method to find a 95% confidence interval for the true proportion of statistics students who smoke. Solution A: Six students out of 25 reported smoking within the past week, so x = 6 and n = 25. Because we are using the “plus-four” method, we will use x = 6 + 2 = 8 and n = 25 + 4 = 29.