Question

Scenario: 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.

Which of the following is correct:

• It is safe to use the z-test for p. ( this is an incorrect answer)
• It is not safe to use the z-test for p, since the sample is not a random sample from the entire population (or cannot be considered as one).
• It is not safe to use the z-test for p since n * p_ois not large enough.
• It is not safe to use the z-test for p since n * (1 - p_o) is not large enough.

Scenario: 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.

Which of the following is correct:

• It is safe to use the z-test for p.
• It is not safe to use the z-test for p, since the sample is not a random sample from the entire population (or cannot be considered as one).
• It is not safe to use the z-test for p, since n * p_ois not large enough.
• It is not safe to use the z-test for p, since n * (1 - p_o) is not large enough.

Scenario: 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.Which of the following is correct:

• It is safe to use the z-test for p.
• It is not safe to use the z-test for p, since the sample is not a random sample from the entire population (or cannot be considered as one).
• It is not safe to use the z-test for p since n * p_ois not large enough.
• It is not safe to use the z-test for p since n * (1 - p_o) is not large enough.

Answer 1

Conditions to be checked-

1. The sampling method must satisfy the random condition.
2. Expected success
3. Expected failure
4. The independence condition which states that when sampling without replacement, we can treat each observation in the sample as independent as long as our sample size is less than 10%.

Scenario-1

1. Here random sampling method is used to obtain sample. Thus it satisfies the random condition.
2. Expected success

So, it is not safe to use z-test for p since n*p is not large enough.

Scenario-2

1. Here random sampling method is used to obtain sample. Thus it satisfies the random condition.
2. Expected success
3. Expected failure
4. Population of U.S. is sufficiently high whose 10% will be higher than 1308.

So, it is safe to use z-test for p.

Scenario-3

1. Here random sampling method is used to obtain sample. Thus it satisfies the random condition.
2. Expected success
3. Expected failure
4. Population of a metropolitan area is sufficiently high whose 10% will be higher than 1200.

So, it is safe to use z-test for p.