Statistics Comparing Two Populations

If the sample sizes are small, but the populations are normally distributed and the population variances are known, the z statistic can be used as the basis for statistical inferences about the difference in two population means using two independent random samples.

• True

• False

If a 90% confidence interval for the difference in the two population means contains zero, then the null hypothesis of zero difference between the two population means cannot be rejected at a 0.10 level of significance

• True

• False

If the populations are normally distributed but the population variances are unknown, the z statistic can be used as the basis for statistical inferences about the difference in two population means using two independent random samples

• True

• False

If the variances of the two populations are equal, it is appropriate to use the “pooled” formula to determine the t statistic for the hypothesis test of the difference in the two population means

• True

• False

In order to construct an interval estimate for the difference in the means of two normally distributed populations with unknown but equal variances, using two independent samples of size n₁ and n₂, we must use a t distribution with (n₁ + n₂) degrees of freedom

• True

• False

Sets of matched samples are also referred to as independent samples

• True

• False

Restaurateur Denny Valentine is evaluating two sites, Raymondville and Rosenberg, for his next restaurant. He wants to prove that Raymondville residents (population 1) dine out more often than Rosenberg residents (population 2). Denny plans to test this hypothesis using a random sample of 81 families from each suburb. His null hypothesis is ___

• s1² < s₂²

• µ₁ – µ₂ > 0

• p₁ – p₂ = 0

• µ₁ – µ₂ = 0

Lucy Baker is analyzing demographic characteristics of two television programs, Lost (population 1) and Heroes (population 2). Previous studies indicate no difference in the ages of the two audiences. (The mean age of each audience is the same.) Lucy plans to test this hypothesis using a random sample of 100 from each audience. Her alternate hypothesis is ___

• m₁ – m₂ < 0

• m₁ – m₂ > 0

• m₁ – m₂ =/ 0

• m₁ – m₂ = 0

A researcher is interested in testing to determine if the mean of population one is greater than the mean of population two. The null hypothesis is that there is no difference in the population means (i.e., the difference is zero). The alternative hypothesis is that there is a difference (i.e., the difference is not equal to zero). He randomly selects a sample of 9 items from population one resulting in a mean of 14.3 and a standard deviation of 3.4. He randomly selects a sample of 14 items from population two resulting in a mean of 11.8 and a standard deviation 2.9. He is using an alpha value of .10 to conduct this test. Assuming that the populations are normally distributed, the degrees of freedom for this problem are ___

• 23

• 21

• 22

• 2