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Explain how hypothesis testing works.
Hypothesis testing uses data from a sample to evaluate a hypothesis about a population. If what is observed in the sample is close to what was expected based on the hypothesis, then there is no reason to question the hypothesis.
The null hypothesis is paired with a mutually exclusive alternative hypothesis, which is what the researcher believes is true. The researcher’s goal is to disprove (reject) the null hypothesis and be “forced” to accept the alternative hypothesis. If the null hypothesis is not rejected, then the researcher doesn’t say it was proven, but states that there wasn’t enough evidence to reject it. This is like a “not guilty” verdict because there wasn’t enough evidence to make a convincing case.
List the six steps to be followed in completing a hypothesis testing.
To complete a hypothesis test, a researcher (1) picks an appropriate test, (2) checks its assumptions to make sure it can be used, (3) lists the null and alternative hypotheses, (4) sets the decision rule, (5) calculates the value of the test statistic, and (6) interprets the results.
Explain and complete a single-sample z test.
A single-sample z test is used to compare a sample mean to a population mean, or a specified value, when the population standard deviation is known. The decision rule says that if the deviation of the sample mean from the specified value can’t be explained by sampling error, then the null hypothesis is rejected.
Explain the decisions that can be made in hypothesis testing.
The conclusion from a hypothesis test may or may not be correct. It’s a correct decision (1) if the null hypothesis should be rejected and it is, or (2) if the null hypothesis should not be rejected and it is not. The potential incorrect decisions are (3) the null hypothesis should not be rejected and it is (Type I error), or (4) the null hypothesis should be rejected and it is not (Type II error).
Error can’t always be avoided, but the probability of one occurring can be determined. The probability of a Type I error, alpha, is usually set, so the error occurs no more than 5% of the time. The probability of Type II error is called beta. Power is the probability of making a correct decision “1.” That is, power is the probability of rejecting the null hypothesis when it should be rejected. Since the goal of research is usually to reject the null hypothesis, researchers want power to be as high as possible.