Chapter 10Inferences on Two Samples

10.1Inference about Means:

Dependent Sampling

A sampling method is independent when the individuals selected for one sample does not dictate which individuals are to be in a second sample. A sampling method is dependent when the individuals selected to be in one sample are used to determine the individuals to be in the second sample.

Dependent samples are often referred to as matched pairs samples.

EXAMPLE Independent versus Dependent SamplingFor each of the following, determine whether the sampling method is independent or dependent.

(a) A researcher wants to know whether the price of a one night stay at a Holiday Inn Express Hotel is less than the price of a one night stay at a Red Roof Inn Hotel. She randomly selects 8 towns where the location of the hotels is close to each other and determines the price of a one night stay.

(b) A researcher wants to know whether the newly issued “state” quarters have a mean weight that is different from “traditional” quarters. He randomly selects 18 “state” quarters and 16 “traditional” quarters. Their weights are compared.

In order to test the hypotheses regarding the mean difference, we need certain requirements to be satisfied.

• A simple random sample is obtained

• the sample data is matched pairs

• the differences are normally distributed or the sample size, n, is large (n > 30).

Step 4: Compare the critical value with the test statistic:

Step 5 : State the conclusion.

EXAMPLE Testing a Claim Regarding Matched Pairs Data

Source: Expedia.com

EXAMPLE Constructing a Confidence Interval for the Mean Difference

Construct a 90% confidence interval for the mean difference in price of Hampton Inn versus La Quinta hotel rooms.

Source: Expedia.com