Suppose that you want to perform a hypothesis test based on independent simple r

Question

Suppose that you want to perform a hypothesis test based on independent simple random samples to compare the means of two populations. Further suppose that the variable under consideration is normally distributed on each of the two populations and that the population standard deviations are unknown. If the sample standard deviations are 3.8 and 6.1, respectively, and the sample sizes are 25 and 60, respectively, would you use the pooled or the non-pooled t-test? Explain your answer. Summary statistics are given for independent simple random samples from two populations. Use the pooled t-interval procedure to obtain the specified confidence interval. 12. A x_1 = 71.6, s_1 = 3.9, n_1 = 11, x_2 = 67.9, s_2 = 3.4, n_2 = 9 Determine a 99% confidence interval.

Explanation / Answer

11.

Below are set of rules whether to use Pooled or Unpooled t tests

• If sample sizes are equal, the pooled and unpooled standard errors are equal. If sample standard deviations are similar, assumption of equal population variance may be reasonable and the pooled procedure could be used.

• If sample sizes are very different, pooled test can be quite misleading unless sample standard deviations are similar. If the smaller standard deviation accompanies the larger sample size, not recommended to use the pooled procedure.

• If sample sizes are very different, the standard deviations are similar, and the larger sample size produced the larger standard deviation, the pooled procedure is acceptable because it will be conservative.

In the problem, sample sizes are very different (25 and 60) and standard deviation are also very much different (3.8 and 6.1), so non-pooled t test should be used.

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