What does the null hypothesis say about the difference between two sample means?
1. Exploratory Data Analysis
Test if two population means are equal The two-sample t-test (Snedecor and Cochran, 1989) is used to determine if two population means are equal. A common application is to test if a new process or treatment is superior to a current process or treatment. There are several variations on this test. Show
SAMPLE 1: NUMBER OF OBSERVATIONS = 249 MEAN = 20.14458 STANDARD DEVIATION = 6.41470 STANDARD ERROR OF THE MEAN = 0.40652 SAMPLE 2: NUMBER OF OBSERVATIONS = 79 MEAN = 30.48101 STANDARD DEVIATION = 6.10771 STANDARD ERROR OF THE MEAN = 0.68717 We are testing the hypothesis that the population means are equal for the two samples. We assume that the variances for the two samples are equal. H0: μ1 = μ2 Ha: μ1 ≠ μ2The absolute value of the test statistic for our example, 12.62059, is greater than the critical value of 1.9673, so we reject the null hypothesis and conclude that the two population means are different at the 0.05 significance level. In general, there are three possible alternative hypotheses and rejection regions for the one-sample t-test:
For our two-tailed t-test, the critical value is t1-α/2,ν = 1.9673, where α = 0.05 and ν = 326. If we were to perform an upper, one-tailed test, the critical value would be t1-α,ν = 1.6495. The rejection regions for three posssible alternative hypotheses using our example data are shown below. Questions Two-sample t-tests can be used to answer the following questions:
Analysis of Variance Case Study Ceramic strength data. Software Two-sample t-tests are available in just about all general purpose statistical software programs. Both Dataplot code and R code can be used to generate the analyses in this section. These scripts use the AUTO83B.DAT data file. What is the null hypothesis for comparing two means?The null hypothesis says that the mean of the differences of the sampling distributions should be equal to zero.
What is the null hypothesis when testing for the significance of the difference between two sample means?Tests of Significance for Two Unknown Means and Known Standard Deviations. which has the standard normal distribution (N(0,1)). The null hypothesis always assumes that the means are equal, while the alternative hypothesis may be one-sided or two-sided.
What does the null hypothesis say about the relationship between the two population means?The null hypothesis states that there is no relationship between two population parameters, i.e., an independent variable and a dependent variable. If the hypothesis shows a relationship between the two parameters, the outcome could be due to an experimental or sampling error.
What is the null value of a difference in means?In the test of the difference of two means, we expect that x̄1 – x̄2 would be close to μ1 – μ2. Therefore, the null hypothesis (which tests the status quo of no difference), is simply H0: μ1 = μ2.
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