There is a statistically significant difference between the sample mean of the two different samples. Rejecting or failing to reject the null hypothesis. A one sample t-test is a hypothesis test for answering questions about the mean where the data are a random sample of independent observations from an underlying normal distribution N(µ, ), where is unknown. Explain (a)t = 1.686 (b) = 0 (c) = 1.515 (d) t = -1.638 OD. As you may recall, an independent-sample t-test attempts to compare an independent sample with another independent sample. If the t-test rejects the null hypothesis (H₀: µ₁=µ₂), it indicates that the groups are highly probably different. 5. Note: In Step 5, I’m using the z-table on this site to solve this problem. If it is less than the significance level (0.05 or 0.01), reject the null hypothesis. If the P-value is less, reject the null hypothesis. For the results of a two sample t-test to be valid, the following assumptions should be met: The 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. If the p-value that corresponds to the test statistic t with (n 1 +n 2-1) degrees of freedom is less than your chosen significance level (common choices are 0.10, 0.05, and 0.01) then you can reject the null hypothesis. $\begingroup$ "fail to reject the null hypothesis" (or something similar) is the way I generally put it on the rare occasions when I formally test a hypothesis and don't reject the null. One Sample T Test Example. We know that the standard potato yield for the given variety is µ=20. • By comparing the null hypothesis to an alternative hypothesis, scientists can either reject or fail to reject the null hypothesis. 0.003 < 0.05, so we have enough evidence to reject the null hypothesis and accept the claim. If we want to examine more groups or larger sample sizes, there are other tests more accurate than t-tests such as z-test, chi-square test or f-test. Two Sample t-test: Assumptions. With hypothesis testing we are setting up a null-hypothesis – the probability that there is no effect or relationship – and then we collect evidence that leads us to either accept or reject that null hypothesis. Rather, all that scientists can determine from a test of significance is that the evidence collected does or does not disprove the null hypothesis. p is lesser in magnitude than 0.05 we need to reject the null hypothesis. Problem Statement: We have the potato yield from 12 different farms. Alternately, simply compute the P-value. If our statistical analysis shows that the significance level is below the cut-off value we have set (e.g., either 0.05 or 0.01), we reject the null hypothesis and accept the alternative hypothesis. As the sample data become progressively dissimilar from the null hypothesis, the absolute value of the t … • The null hypothesis cannot be positively proven. Click to select your answer State whether the standardized test statistict indicates that you should reject the null hypothesis. Let’s take an example from a blood pressure dataset. Let's return finally to the question of whether we reject or fail to reject the null hypothesis. Paired T-Test. In general, there are three possible alternative hypotheses and rejection regions for the one-sample t-test: The null hypothesis for the one sample t-test is: H 0. µ = µ 0. where µ 0 is known. Reject Hy, because t< 1.593 (c) Fort=1.515, should you reject or fail to reject the null hypothesis? 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