Select the analysis options for 1-Sample Z

Stat > Basic Statistics > 1-Sample Z > Options

Specify the confidence level for the confidence interval or define the alternative hypothesis.

Confidence level

In Confidence level, enter the level of confidence for the confidence interval.

Usually, a confidence level of 95% works well. A 95% confidence level indicates that, if you take 100 random samples from the population, the confidence intervals for approximately 95 of the samples will contain the population parameter.

For a given set of data, a lower confidence level produces a narrower confidence interval, and a higher confidence level produces a wider confidence interval. The width of the interval also tends to decrease with larger sample sizes. Therefore, you may want to use a confidence level other than 95%, depending on your sample size.
  • If your sample size is small, a 95% confidence interval may be too wide to be useful. Using a lower confidence level, such as 90%, produces a narrower interval. However, the likelihood that the interval contains the population mean decreases.
  • If your sample size is large, consider using a higher confidence level, such as 99%. With a large sample, a 99% confidence level may still produce a reasonably narrow interval, while also increasing the likelihood that the interval contains the population mean.

Alternative hypothesis

From Alternative hypothesis, select the hypothesis that you want to test:
Mean < hypothesized mean

Use this one-sided test to determine whether the population mean is less than the hypothesized mean, and to get an upper bound. 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 determine whether the mean concentration of solids in water is less than 22.4 mg/L. This 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.

Mean ≠ hypothesized mean

Use this two-sided test to determine whether the population mean differs from the hypothesized mean, and to get a two-sided confidence interval. A 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 from 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.

Mean > hypothesized mean

Use this one-sided test to determine whether the population mean is greater than the hypothesized mean, and to get a lower bound. This one-sided test has greater power than a two-sided test, but it cannot detect whether the population mean is less 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.

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