Go to the row that represents the ones digit and the first digit after the decimal point (the tenths digit) of your z-value. When you hear a researcher say their results are found to be statistically significant, look for the p-value and make your own decision; the researcher’s predetermined significance level may be different from yours. If the p-value isn’t stated, ask for it.

For each (x, y) pair in the data set, take x minus and y minus , and multiply them together to get .If the data show a downhill pattern as you move from left to right, this indicates a negative relationship between X and Y. As the X-values increase (move right) the Y-values decrease (move down) by a certain amount. Note that if the alternative hypothesis is the less-than alternative, you reject H0 only if the test statistic falls in the left tail of the distribution (below –2). Similarly, if Ha is the greater-than alternative, you reject H0 only if the test statistic falls in the right tail (above 2).

After you calculate a confidence interval, make sure you always interpret it in words a non-statistician would understand. That is, talk about the results in terms of what the person in the problem is trying to find out — statisticians call this interpreting the results “in the context of the problem.” Use the z -table to find where the row for 1.5 intersects with the column for 0.00, which is 0.9332. Because the z -table gives you only "less than" probabilities, subtract P( Z< 1.5) from 1 (remember that the total probability for the normal distribution is 1.00, or 100%): P ( Z ≥ 1.5) = 1 – P ( Z< 1.5) How to use the t-table to find right-tail probabilities and p-values for hypothesis tests involving t: For example, suppose you want to find p(Z < 2.13). Using the z-table below, find the row for 2.1 and the column for 0.03. Intersect that row and column to find the probability: 0.9834. Therefore p(Z < 2.13) = 0.9834. After delving into the process of how to find a p-value from a test statistic and understanding its significance in hypothesis testing, we now transition to a critical stage: making conclusions.

In either of these situations, a confidence interval for the difference in the two population means is Your 95 percent confidence interval for the mean length of walleye fingerlings in this fish hatchery pond is 7.5 inches ± 0.45 inches.

In this article I explore linear relationships only. A linear relationship between X and Y exists when the pattern of X- and Y-values resembles a line, either uphill (with a positive slope) or downhill (with a negative slope). Other types of trends may exist in addition to the uphill/downhill linear trends (for example, curves or exponential functions); however, these trends are beyond the scope of this book. The good news is that many relationships do fall under the uphill/downhill linear scenario. Using the rest of the information you are given, find the confidence interval for the difference in mean cob length for the two brands:A matched-pairs design with 44 total observations has 22 pairs. The degrees of freedom is one less than the number of pairs: n – 1 = 22 – 1 = 21. If Ha contains a not-equal-to alternative, find the probability that Z is beyond your test statistic and double it. There are two cases: Clear and concise step-by-step procedures that intuitively explain how to work through statistics problems.