Learn by Doing: Proportions (Step 2) Verify Conditions
In each of the following scenarios, you need to decide whether it is appropriate to use the z-test for the population proportion p, and if not, which condition is violated.
Scenario 1: The UCLA Internet Report (February 2003) estimated that roughly 8.7% of Internet users are extremely concerned about credit card fraud when buying online. Has that figure changed since? To test this, a random sample of 100 Internet users was chosen. When interviewed, 10 said that they were extremely worried about credit card fraud when buying online. Let p be the proportion of all Internet users who are concerned about credit card fraud.
Scenario 2: The UCLA Internet Report (February 2003) estimated that a proportion of roughly .75 of online homes are still using dial-up access, but claimed that the use of dial-up is declining. Is that really the case? To examine this, a follow-up study was conducted a year later in which out of a random sample of 1,308 households that had an Internet connection, 804 were connecting using a dial-up modem. Let p be the proportion of all U.S. Internet-using households that have dial-up access.
Scenario 3: According to the UCLA Internet Report (February 2003) the use of the Internet at home is growing steadily. The report estimated that roughly 59.3% of households in the Unites States have Internet access at home. Has that trend continued since the report was released? To study this, a random sample of 1,200 households from a big metropolitan area was chosen, and it was found that 972 had an Internet connection. Let p be the proportion of U.S. households that have Internet access.
This document is linked from Proportions (Step 2).