# Select the analysis options for 2-Sample t

Stat > Basic Statistics > 2-Sample t > Options

Specify the confidence level for the confidence interval, specify the null hypothesis, define the alternative hypothesis, or specify whether you can assume equal variances.

## 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 difference.

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 difference 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 difference.

## Hypothesized difference

Enter a value in Hypothesized difference. The hypothesized difference defines your null hypothesis. Think of this value as a target value or a reference value. For example, an analyst enters 75 to test whether two types of steel have average strengths that are different by 75 psi (H0: μ1– μ2 = 75).

## Alternative hypothesis

From Alternative hypothesis, select the hypothesis that you want to test:
Difference < hypothesized difference

Use this one-sided test to determine whether the difference between the population means of sample 1 and sample 2 is less than the hypothesized difference, and to get an upper bound. This one-sided test has greater power than a two-sided test, but it cannot detect whether the difference is greater than the hypothesized difference.

For example, an engineer uses this one-sided test to determine whether the mean difference in strength of plastic sheeting from two suppliers is less than 0. This one-sided test has greater power to detect whether the difference in strength is less than 0, but it cannot detect whether the difference is greater than 0.

Difference ≠ hypothesized difference

Use this two-sided test to determine whether the difference in population means differs from the hypothesized difference, and to get a two-sided confidence interval. This two-sided test can detect differences that are less than or greater than the hypothesized difference, but it has less power than a one-sided test.

For example, a bank manager wants to know whether the mean customer satisfaction ratings at two banks differ. Because any difference in the ratings is important, the manager uses this two-sided test to determine whether the rating at one bank is greater than or less than the rating of the other bank.

Difference > hypothesized difference

Use this one-sided test to determine whether the difference between the population means of sample 1 and sample 2 is greater than the hypothesized difference and to get an upper bound. This one-sided test has greater power than a two-sided test, but it cannot detect whether the difference is less than the hypothesized difference.

For example, a technician uses this one-sided test to determine whether the mean difference between the speeds of two filling machines is greater than 0 seconds per box. This one-sided test has greater power to detect whether the difference in speed is greater than 0, but it cannot detect whether the difference is less than 0.

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

## Assume equal variances

Select Assume equal variances when the variances of the two populations are equal or when the samples are about the same size. If the two population variances are truly equal, then the 2-sample t-test with the assumption of equal variances is slightly more powerful than the 2-sample t-test without the assumption of equal variances. If you assume equal variances when the variances are not equal or when the sample sizes are very different, serious error can occur.

When you assume equal variances, Minitab uses the pooled estimate of the sample standard deviations.

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