Question

a researcher wishes to test a hypothesis that compares family incomes between two cities. he sampled 20 households from each city. he was given the population standard deviation of family income for each city. the income for each city follows a normal distribution. this is an example of:_______.

Answer 1

The scenario describes a hypothesis test for comparing two population means from independent samples with known population standard deviations, normally distributed, using a z-test.

Step-by-step explanation:

The scenario presented is an example of a hypothesis test for comparing two population means from independent samples with known population standard deviations. This type of hypothesis testing assumes both populations follow a normal distribution. The normal distribution is used here for the difference between the sample means, represented as the random variable X₁ - X₂. In situations where the population standard deviations are known, the z-test is the appropriate statistical test to use.

An essential requirement for this test is that the samples are independently and randomly selected, and that the populations they are drawn from have approximately equal standard deviations. If the populations from which the samples were drawn were to have different standard deviations, additional testing would be required to confirm the assumption of equal variances before conducting a z-test.

Here's a practical example akin to the scenario described: Two cities are compared based on family incomes. The researcher uses the normal distribution for hypothesis testing, given that the income for each city follows a normal distribution and the population standard deviations are known. While it is unusual to know the population standard deviations in practice, this theoretical setup allows for a straightforward application of the z-test for comparing the two means.