Practice Calculating pValues
Hypothesis testing can seem like a plugandchug operation, but that can take you only so far. Remember that a small pvalue comes from a large test statistic, and both mean rejecting H_{0}. Calculate pvalues in the following problems.
Sample questions

A researcher has a less than alternative hypothesis and wants to run a single sample mean ztest. The researcher calculates a teststatistic of z = –1.5 and then uses a Ztable to find a corresponding area of 0.0668, which is the area under the curve to the left of that value of z.
What is the pvalue in this case?
Answer: 0.0668
Using the ztable, find –1.5 in the lefthand column, and then go across the row to the column for 0.00, where the value is 0.0668. This is the proportion of the curve area that’s to the left of (less than) the test statistic value of z that you’re looking up. In this case, the alternative hypothesis is a less than hypothesis, so you can read the pvalue from the table without doing further calculations.

Suppose that a researcher has a not equal to alternative hypothesis and calculates a test statistic that corresponds to z = –1.5 and then finds, using a Ztable, a corresponding area of 0.0668 (the area under the curve to the left of that value of z).
What is the pvalue in this case?
Answer: 0.1336
Using the ztable, find –1.5 in the lefthand column, and then go across the row to the column for 0.00, where the value is 0.0668. This is the proportion of the curve area that’s to the left of (less than) the value of z you’re looking up.
In this case, the alternative hypothesis is a not equal to hypothesis, so you double the outlying tail quantity (area below the zvalue of –1.5) to get the pvalue.

A researcher has a not equal to alternative hypothesis and calculates a test statistic that corresponds to z = –2.0. Using a Ztable, the researcher finds a corresponding area of 0.0228 to the left of –2.0.
What is the pvalue in this case?
Answer: 0.0456
Using the ztable, find –2.0 in the lefthand column, and then go across the row to the column for 0.0, where the value is 0.0228. This is the proportion of the curve area that’s to the left of (less than) the value of z you’re looking up.
In this case, the alternative hypothesis is a not equal to hypothesis, so you double the outlying tail quantity (area below the zvalue of –2.0) to get the pvalue.

A scientist with a not equal to alternative hypothesis calculates a test statistic that corresponds to z = 1.1. Using a Ztable, the scientist finds that this corresponds to a curve area of 0.8643 (to the left of the test statistic value).
What is the pvalue in this case?
Answer: 0.2714
Using the ztable, find 1.1 in the lefthand column, then go across the row to the column for 0.0, where the value is 0.8643. This is the area under the curve to the left of the z value of 1.1. Because total area under the curve equals 1, the area above z in this case is 1 – 0.8643 = 0.1357.
In this case, the alternative hypothesis is a not equal to hypothesis, so you double the outlying tail quantity (area above the zvalue of 1.1) to get the pvalue.
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