# How do you find the test statistic for a population proportion?

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:

## How do you find the test statistic for a population proportion?

The basic procedure is:

1. State the null hypothesis H0 and the alternative hypothesis HA.
2. Set the level of significance .
3. Calculate the test statistic: z = p ^ − p o p 0 ( 1 − p 0 ) n.
4. Calculate the p-value.
5. Make a decision. Check whether to reject the null hypothesis by comparing p-value to .

### What is the 95% confidence interval for the population proportion?

The 95% confidence interval for the true binomial population proportion is ( p′ – EBP, p′ + EBP) = (0.810, 0.874).

#### What test statistic is used for constructing a confidence interval on the population proportion?

To use the standard error, we replace the unknown parameter p with the statistic p̂. The result is the following formula for a confidence interval for a population proportion: p̂ +/- z* (p̂(1 – p̂)/n)0.5.

What is the test statistic for confidence interval?

So, if your significance level is 0.05, the corresponding confidence level is 95%. If the P value is less than your significance (alpha) level, the hypothesis test is statistically significant. If the confidence interval does not contain the null hypothesis value, the results are statistically significant.

What is the test statistic for proportion?

Statistics – One Proportion Z Test The test statistic is a z-score (z) defined by the following equation. z=(p−P)σ where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and σ is the standard deviation of the sampling distribution.

## How do you find P-value from proportion?

Since we have a two-tailed test, the P-value is the probability that the z-score is less than -1.75 or greater than 1.75. We use the Normal Distribution Calculator to find P(z < -1.75) = 0.04, and P(z > 1.75) = 0.04. Thus, the P-value = 0.04 + 0.04 = 0.08.

### What is the formula for the confidence interval for the population proportion?

To calculate the confidence interval, you must find p′, q′, andEBP. p′ = 0.842 is the sample proportion; this is the point estimate of the population proportion. Since CL = 0.95, then α = 1 – CL = 1 – 0.95 = 0.05 (α) = 0.025.

#### What is the formula for z test proportion?

How is the confidence interval for a population proportion determined?

Here the value of z* is determined by our level of confidence C. For the standard normal distribution, exactly C percent of the standard normal distribution is between -z* and z*. Common values for z* include 1.645 for 90% confidence and 1.96 for 95% confidence.

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 confidence level for proportion statology?

The following table shows the z-value that corresponds to popular confidence level choices: Confidence Level z-value 0.90 1.645 0.95 1.96 0.99 2.58

### 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.
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