Two-Sample T-Interval Procedure

Question

The table provides summary statistics for two independent samples. To construct a 95% confidence interval for the difference between the two population means, which of the following is a necessary step, given that the population standard deviations are unknown?

| Group         | Sample Size | Sample Mean | Sample Standard Deviation |
|---------------|-------------|-------------|---------------------------|
| Department 1  |     30      |    12.3     |           3.5             |
| Department 2  |     30      |    7.6      |           3.4             |

Accepted Answer

Use the t-distribution with degrees of freedom approximated by taking the minimum of $$n_1-1$$ and $$n_2-1$$ and compute the standard error as $$\sqrt{(s_1^2/n_1) + (s_2^2/n_2)}$$.

Answer

Use the normal distribution regardless of sample sizes when the population standard deviations are unknown.

Answer

Calculate a pooled variance and then use the z-distribution with degrees of freedom equal to $$n_1+n_2-1$$.

Answer

Use a chi-square distribution to adjust for the variance in the sample standard deviations.

Two-Sample T-Interval Procedure

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