This test is used when the varaible is numerical (for example, cost of goods, earnings, stock price) and two populations or groups are being compared. This Test Statistic Comparing Two Population Means Calculator calculates the test statistic when comparing two population means. Test Statistic Comparing Two Population Means: Test Statistic Comparing Two Means Calculator Plugging these values into the formula gives us, And let's say that the standard deviation is 1.7. Let's say we areĭealing with a sample size of 100 students. So in this example, the mean, x, is 15 ($15 for the average working college students spend a day on food). The test statistic for one population mean, which is, Z= ( x - μ 0)/(σ/√ n). So going back to this example, we use the formula for So the alternative hypothesis is that working college students actually spend $20 a day on food instead of the $15 that the economist believes In this example, we'll say that H a is equal to The alternative hypothesis, H a, is either μ > 15, μ < 15, or μ ≠ 15. The economist is claiming that this average amount is equal to $15. Working college students spend a day on food. μ represents the average money in dollars amount that all The null hypothesis in this example for this economist is, H 0= μ= $15. The variable, money, is numerical and the population is Let's say that an economist, Economist William German, believes that students who work and go to college only spend, on average, Because this p-value is less than α, you declare statistical significance and reject the null hypothesis.ĭifferent hypothesis tests use different test statistics based on the probability model assumed in the null hypothesis.The Test Statistic for One Population Mean Calculator is a calculator that is used when the variable is numerical and only one population or group This Z-value corresponds to a p-value of 0.0124. Suppose you perform a two-tailed Z-test with an α of 0.05, and obtain a Z-statistic (also called a Z-value) based on your data of 2.5. This causes the test's p-value to become small enough to reject the null hypothesis.įor example, the test statistic for a Z-test is the Z-statistic, which has the standard normal distribution under the null hypothesis. When the data show strong evidence against the assumptions in the null hypothesis, the magnitude of the test statistic becomes too large or too small depending on the alternative hypothesis. The sampling distribution of the test statistic under the null hypothesis is called the null distribution. A test statistic contains information about the data that is relevant for deciding whether to reject the null hypothesis. Its observed value changes randomly from one random sample to a different sample. The test statistic is used to calculate the p-value.Ī test statistic measures the degree of agreement between a sample of data and the null hypothesis. The test statistic compares your data with what is expected under the null hypothesis. You can use test statistics to determine whether to reject the null hypothesis. A test statistic is a random variable that is calculated from sample data and used in a hypothesis test.