t-test – Quality control inspectors are investigating the number of peanuts in each (small) bag of trail mix. If there are too few peanuts in the bag, customers will complain. If there are too many, then the company will lose money on each bag of trail mix sold. The peanuts are put into bags by an Automatic Peanut Packer. We know that the machine works in such a way that the number of peanuts in each bag has a normal distribution with variance 16.16 (σ =4.02). On the average, the bags are supposed to have 7 peanuts. Our mission is to test the null hypothesis that the mean is μ is equal to 7. We have n = 13 observations from the mean:
9, 11, 6, 10, 7, 4, 0, 7, 8, 6, 8, 2, 18
The sample average is 7.38. Is that close enough to 7 so that we should accept the hypothesis? Or is it too far away? We know that if the hypothesis is true, then will have a normal distribution with mean μ = 7 and variance 16.16/n. So, there …show more content…
So, t will be our test statistic. In our case, the computed value of t is .341, which is well within the zone of acceptance. So we can accept the hypothesis that μ = 7.
The Independent Samples t-Test can only associate the means for two (and only two) groups. It cannot make comparisons among more than two groups. If you wish to compare the means across more than two groups, you will likely want to run an ANOVA.
The Dependent Samples t-test (also called the paired t-test or paired-samples t-test) compares the means of two related groups to detect whether there are any statistically significant differences between these
9, 11, 6, 10, 7, 4, 0, 7, 8, 6, 8, 2, 18
The sample average is 7.38. Is that close enough to 7 so that we should accept the hypothesis? Or is it too far away? We know that if the hypothesis is true, then will have a normal distribution with mean μ = 7 and variance 16.16/n. So, there …show more content…
So, t will be our test statistic. In our case, the computed value of t is .341, which is well within the zone of acceptance. So we can accept the hypothesis that μ = 7.
The Independent Samples t-Test can only associate the means for two (and only two) groups. It cannot make comparisons among more than two groups. If you wish to compare the means across more than two groups, you will likely want to run an ANOVA.
The Dependent Samples t-test (also called the paired t-test or paired-samples t-test) compares the means of two related groups to detect whether there are any statistically significant differences between these