Select the analysis options for Power and Sample Size for 1-Sample Z

Stat > Power and Sample Size > 1-Sample Z > Options

Select the alternative hypothesis or specify the significance level for the test.

Alternative Hypothesis
From Alternative Hypothesis, select the hypothesis that you want to test:
  • Less than: Use this one-sided test to determine whether the population mean is less than the hypothesized mean. This one-sided test has greater power than a two-sided test, but it cannot detect whether the population mean is greater than the hypothesized mean.

    For example, a quality analyst uses this one-sided test to be certain that the mean concentration of solids in water is less than 22.4 mg/L. The one-sided test has greater power to determine whether the mean is less than 22.4 mg/L, but it cannot detect whether the mean is greater than 22.4 mg/L.

  • Not equal: Use this two-sided test to determine whether the population mean differs from the hypothesized mean. This two-sided test can detect differences that are less than or greater than the hypothesized value, but it has less power than a one-sided test.

    For example, an engineer wants to know if the mean length of pencils is different than the target of 18.85 cm. Because any difference from the target is important, the engineer uses this two-sided test to determine whether the mean is greater than or less than the target.

  • Greater than: Use this one-sided test to determine whether the population mean is greater than the hypothesized mean.

    For example, a hospital administrator uses this one-sided test to determine whether the mean rating on a patient satisfaction survey is greater than 90. This one-sided test has greater power to determine whether the mean rating is greater than 90, but it cannot detect whether the mean rating is less than 90.

For more information on selecting a one-sided or two-sided alternative hypothesis, go to About the null and alternative hypotheses.

Significance level

Use the significance level to minimize the power value of the test when the null hypothesis (H0) is true. Higher values for the significance level give the test more power, but also increase the chance of making a type I error, which is rejecting the null hypothesis when it is true.

Usually, a significance level (denoted as α or alpha) of 0.05 works well. A significance level of 0.05 indicates that the risk of concluding that a difference exists—when, actually, no difference exists—is 5%. It also indicates that the power of the test is 0.05 when there is no difference.
  • Choose a higher significance level, such as 0.10, to be more certain that you detect any difference that possibly exists. For example, a quality engineer compares the stability of new ball bearings with the stability of current bearings. The engineer must be highly certain that the new ball bearings are stable because unstable ball bearings could cause a disaster. Therefore, the engineer chooses a significance level of 0.10 to be more certain of detecting any possible difference in the stability of the ball bearings.
  • Choose a lower significance level, such as 0.01, to be more certain that you detect only a difference that actually exists. For example, a scientist at a pharmaceutical company must be very certain that a claim that the company's new drug significantly reduces symptoms is true. The scientist chooses a significance level of 0.01 to be more certain that any significant difference in symptoms does exist.
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