Explain the difference between a one-tailed and a two-tailed test. Suppose a sam

Question

Explain the difference between a one-tailed and a two-tailed test. Suppose a sample of the US population is taken and the heights of every individual in the study are taken. Give an example of a hypothesis that would require a one-tailed test and a hypothesis that would require a two-tailed test. Define a Type I error and a Type II error. If a business commissioned a study on whether or not to adopt a new technology, would a Type I error or Type II error be worse? Explain. In hypothesis testing, why can't the hypothesis be proven true?

Explanation / Answer

Two-tailed tests -

A Two-tailed test is associated to an alternative hypotheses for which the sign of the potential difference is unknown. For example, suppose we wish to compare the averages of two samples A and B. Before setting up the experiment and running the test, we expect that if a difference between the two averages is highlighted, we do not really know whether A would be higher than B or the opposite. This drives us to choose a two-tailed test, associated to the following alternative hypothesis: Ha: average(A) average(B). Two-tailed tests are by far the most commonly used tests.

One-tailed tests -

A One-tailed test is associated to an alternative hypothesis for which the sign of the potential difference is known before running the experiment and the test. In the example described above, the alternative hypothesis related to a one-tailed test could be written as follows: average(A) < average(B) or average(A) > average(B), depending on the expected direction of the difference.

Type I error -

A type I error, or false positive, is asserting something as true when it is actually false. This false positive error is basically a “false alarm” – a result that indicates a given condition has been fulfilled when it actually has not been fulfilled (i.e., erroneously a positive result has been assumed).

Type II error -

A type II error occurs when the null hypothesis is false, but erroneously fails to be rejected. Let me say this again, a type II error occurs when the null hypothesis is actually false, but was accepted as true by the testing.

A type II error, or false negative, is where a test result indicates that a condition failed, while it actually was successful.   A Type II error is committed when we fail to believe a true condition.

For problem given as t above ,It’s hard to create a blanket statement that a type I error is worse than a type II error, or vice versa. The severity of the type I and type II errors can only be judged in context of the null hypothesis, which should be thoughtfully worded to ensure that we’re running the right test.

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