Which of these statements is the null hypothesis for an F test
The F-test formula one may use to perform the statistical test that helps the person conducting the test find whether the two population sets having the normal distribution of the data points have the same standard deviation. Show F-Test is any test that uses F-distribution. F-value is a value on the F-distribution. Various statistical tests generate an F value. The value can determine whether the test is statistically significant. For example, to compare two variances, one has to calculate the ratio of the two variances, which is as under: F Value = Larger Sample Variance / Smaller Sample Variance = σ12 / σ22 You are free to use this image on your website, templates, etc., Please provide us with an attribution linkHow to Provide Attribution?Article Link to be Hyperlinked While F-test in ExcelF-test In ExcelF-test in excel is a statistical tool that helps us decide whether the variances of two populations having normal distribution are equal or not. F-test is an essential part of the analysis of variance (ANOVA) model.read more, we need to frame the null and alternative hypotheses. Then, we need to determine the level of significance under which the test has to carry. Subsequently, we must determine the degrees of freedomDegrees Of FreedomDegrees of freedom (df) refers to the number of independent values (variable) in a data sample used to find the missing piece of information (fixed) without violating any constraints imposed in a dynamic system. These nominal values have the freedom to vary, making it easier for users to find the unknown or missing value in a dataset.read more of the numerator and denominator. It will help determine the F-table value. The F-value seen in the table is then compared to the calculated F-value to determine whether or not to reject the null hypothesis. Table of contentsStep by Step Calculation of an F-testBelow are the steps where the F-Test formula is used for the null hypothesis that the variances of two populations are equal:
ExamplesYou can download this F Test Formula Excel Template here – Example #1A statistician was carrying out an F-Test. He got the F statistic as 2.38. The degrees of freedom obtained by him were 8 and 3. Find out the F value from the F Table and determine whether we can reject the null hypothesis at a 5% significance level (one-tailed test). Solution: We must look for 8 and 3 degrees of freedom in the F Table. The F critical value obtained from the table is 8.845. Since the F statistic (2.38) is lesser than the F Table Value (8.845), we cannot reject the null hypothesis. Example #2An insurance company sells health insurance and motor insurance policies. Customers pay premiums for these policies. The CEO of the insurance company wonders if premiums paid by either of the insurance segments (health insurance and motor insurance) are more variable than another. He finds the following data for premiums paid: Conduct a two-tailed F-test with a level of significance of 10%. Solution:
Alternate Hypothesis Ha: σ12 ≠ σ22
df2 = n2 – 1 = 51-1 = 50
Example #3The bank has a head office in Delhi and a branch in Mumbai. There are long customer queues at one office, while customer queues are short at the other. The Operations Manager of the bank wonders if the customers at one branch are more variable than the number of customers at another. He carries out a research study of customers. The variance of Delhi head office customers is 31, and that for the Mumbai branch is 20. The sample size for the Delhi head office is 11, and that for the Mumbai branch is 21. Carry out a two-tailed F-test with a level of significance of 10%. Solution:
Alternate Hypothesis Ha: σ12 ≠ σ22
df2 = n2 – 1 = 21-1 = 20
Relevance and UsesOne can use the F-Test formula in a wide variety of settings:
F-Test Formula in Excel (with Excel Template)Workers in an organization pay daily wages. However, the organization’s CEO is concerned about the wage variability between males and females in the organization. Below are the data taken from a sample of males and females. Conduct a one-tailed F-Test at a 5% level of significance. Solution:
It will display the values for F statistic and F table value along with other data.
Note 1: The variance of “Variable 1” has to be higher than that of “Variable 2.” Otherwise, calculations made in Excel will be wrong. If not, then swap the data. Note 2: If the “Data Analysis” button is unavailable in Excel, go to File > Options. Under Add-ins, select Analysis ToolPak and click on the Go button. Next, check “Analysis Tool Pack” and click on “OK.” Note 3: Excel uses a formula to calculate the F table value. Its syntax is: Recommended ArticlesThis article is a guide to F-Test Formula. Here, we learn how to perform an F-Test to determine whether or not to reject the null hypothesis, along with examples and a downloadable Excel template. You can learn more about statistical modeling from the following articles: –
|