Statistics For Dummies, 2nd Edition (For Dummies (Lifestyle))

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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? 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) Bivariate data is typically organized in a graph that statisticians call a scatter­plot. A scatterplot has two dimensions, a horizontal dimension (the X-axis) and a vertical dimension (the Y-axis). Both axes are numerical; each one contains a number line. In the following sections, I explain how to make and interpret a scatterplot.

In statistics, a confidence interval is an educated guess about some characteristic of the population. A confidence interval contains an initial estimate plus or minus a margin of error (the amount by which you expect your results to vary, if a different sample were taken). Go to the column that represents the second digit after the decimal point (the hundredths digit) of your z-value. First, find the t-value for which you want the right-tail probability (call it t), and find the sample size (for example, n). However, if you plan to make decisions about Ho by comparing the p-value to your significance level, you must decide on your significance level ahead of time. It wouldn’t be fair to change your cutoff point after you’ve got a sneak peek at what’s happening in the data.For example, suppose you have the data set (3, 2), (3, 3), and (6, 4). You calculate the correlation coefficient r via the following steps. (Note for this data the x-values are 3, 3, 6, and the y-values are 2, 3, 4.) 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. 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. If the scatterplot doesn’t show that there’s at least somewhat of a linear relationship, the correlation doesn’t mean much. Why measure the amount of linear relationship if there isn’t much of one? is 8.5 – 7.5 = +1 inch. This means the average for Corn-e-stats minus the average for Stats-o-sweet is positive, making Corn-e-stats the larger of the two varieties, in terms of this sample. Is that difference enough to generalize to the entire population, though? That’s what this confidence interval is going to help you decide.

Noting that the total area under any normal curve (including the standardized normal curve) is 1, it follows that p(Z < 2.13) + p(Z > 2.13) =1. Therefore, p(Z > 2.13) = 1 – p(Z < 2.13) which equals 1 – 0.9834 which equals 0.0166. 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. 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.When you are wondering how to find a p-value with a test statistic, remember that the formula involves using your test statistic to identify a probability on a Z-table corresponding to the strength of evidence against the null hypothesis.

Can one statistic measure both the strength and direction of a linear relationship between two variables? Sure! Statisticians use the correlation coefficient to measure the strength and direction of the linear relationship between two numerical variables X and Y. The correlation coefficient for a sample of data is denoted by r. You might have heard this expressed as "interpreting correlation," an "r interpretation," or a "correlation interpretation." For both groups, you took random sample of 15 cobs, with the Corn-e-stats variety averaging 8.5 inches, and Stats-o-sweet 7.5 inches. So the information you have is:

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). When you perform a hypothesis test in statistics, a p-value helps you determine the significance of your results. Hypothesis tests are used to test the validity of a claim that is made about a population. This claim that’s on trial, in essence, is called the null hypothesis. Using the t-table, locate the row with 14 degrees of freedom and look for 2.35. However, this exact value doesn’t lie in this row, so look for the values on either side of it: 2.14479 and 2.62449. The upper-tail probabilities appear in the column headings; the column heading for 2.14479 is 0.025, and the column heading for 2.62449 is 0.01.