To find the probability that Z is between two values, use the z -table to find the probabilities corresponding to each z -value, and then find the difference between the probabilities. But say your p-value had been something like 0.026. A reader with a personal cutoff point of 0.05 would reject Ho in this case because the p-value (of 0.026) is less than 0.05. The reader's conclusion would be that the proportion of women with varicose veins isn’t equal to 0.25; according to Ha, in this case, you conclude it’s less than 0.25, and the results are statistically significant.

wikiHow is a “wiki,” similar to Wikipedia, which means that many of our articles are co-written by multiple authors. To create this article, 28 people, some anonymous, worked to edit and improve it over time. Because the z -table gives you only "less than" probabilities, find the difference between the probability less than 1.0 and the probability less than –0.5: P (–0.5 ≤ Z ≤ 1.0) = P ( Z ≤ 1.0) – P ( Z ≤ –0.50) If the p-value is between 0.05 and 0.01 (but not super close to 0.05), the results are considered statistically significant — reject Ho. Understanding how to get a p-value from a test statistic is essential for assessing whether the results of your test are likely to have occurred by chance, assuming the null hypothesis is true. However, this may lead you to wonder whether it’s okay to say “Accept Ho” instead of “Fail to reject Ho.” The answer is a big no.In the following, I discuss correlation, a statistic measuring the strength and direction of a linear relationship between two variables; in particular, how to calculate and interpret correlation and understand its most important properties. The above figure shows examples of what various correlations look like, in terms of the strength and direction of the relationship. Figure (a) shows a correlation of nearly +1, Figure (b) shows a correlation of –0.50, Figure (c) shows a correlation of +0.85, and Figure (d) shows a correlation of +0.15. p-values very close to the cutoff (0.05) are considered to be marginal (could go either way). Always report the p-value so your readers can draw their own conclusions. A t-value of 2.35, from a t-distribution with 14 degrees of freedom, has an upper-tail (“greater than”) probability between which two values on the t-table?

Then, go to the top of the columns containing the two t-values from Step 2. The right-tail (greater-than) probability for your t-value is somewhere between the two values at the top of these columns. For example, your t = 1.60 is between t-values 1.44 and 1.94 (df = 6); so the right tail probability for your t is between 0.10 (column heading for t = 1.44); and 0.05 (column heading for t = 1.94).Look at the bottom row of the table where the percentages are shown. Find your % confidence level there. Divide the result by n – 1, where n is the number of (x, y) pairs. (It’s the same as multiplying by 1 over n – 1.) To draw conclusions about Ho (reject or fail to reject) based on a p-value, you need to set a predetermined cutoff point where only those p-values less than or equal to the cutoff will result in rejecting Ho. This cutoff point is called the alpha level (α), or significance level for the test. You didn’t have enough evidence to say the proportion of women with varicose veins is less than 0.25 (your alternative hypothesis). This isn’t declared to be a statistically significant result. Similarly, if you’ve got a negative test statistic, its p-value only accounts for the less-than portion of the not-equal-to alternative; double it to also account for the greater-than portion.

Here, you want the probability that Z is between –0.5 and 1.0. First, use the z -table to find the value where the row for –0.5 intersects with the column for 0.00, which is 0.3085. Then, find the value where the row for 1.0 intersects with the column for 0.00, which is 0.8413. 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. Although the street definition of correlation applies to any two items that are related (such as gender and political affiliation), statisticians use this term only in the context of two numerical variables. The formal term for correlation is the correlation coefficient. Many different correlation measures have been created; the one used in this case is called the Pearson correlation coefficient (but from now on I’ll just call it the correlation). Your 95 percent confidence interval for the mean length of walleye fingerlings in this fish hatchery pond is 7.5 inches ± 0.45 inches.The t-table (for the t-distribution) is different from the z-table (for the z-distribution). Make sure you understand the values in the first and last rows. Finding probabilities for various t-distributions, using the t-table, is a valuable statistics skill. Here, you want the probability that Z is between –1.0 and 1.0. First, use the z-table to find the value where the row for –1.0 intersects with 0.00, which is 0.1587. Then, find the value where the row for 1.0 intersects with the column for 0.00, which is 0.8413. You can use the z-score table to find a full set of "less-than" probabilities for a wide range of z-values using the z-score formula. Below you will find both the positive z-score and negative z-score table. The problem examples below the table will help you learn how to use it. You know that the average length is 7.5 inches, the sample standard deviation is 2.3 inches, and the sample size is 10. This means