A sample of households in a community is selected at random from the telephone directory. In this community, 4 % 4% of households have no telephone, 10 % 10% have only cell phones, and another 25 % 25% have unlisted telephone numbers. The sample will certainly suffer from a. false responses. b. undercoverage. c. nonresponse. d. nonresponse, undercoverage and false responses.

Question

Riley Roberts

Mathematics

9 August, 10:09

A sample of households in a community is selected at random from the telephone directory. In this community, 4 % 4% of households have no telephone, 10 % 10% have only cell phones, and another 25 % 25% have unlisted telephone numbers. The sample will certainly suffer from a. false responses. b. undercoverage. c. nonresponse. d. nonresponse, undercoverage and false responses.

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Logan Cisneros · Answer 1

The sample will certainly suffer from under coverage bias.

Step-by-step explanation:

In a random sample selected every value of the population has an equal probability of being selected.

If there are some values that have 0 probability of being selected then there is a bias in the sampling method.

This type of bias happens when some values are not considered to be included in the sampling frame. This kind of bias is known as under coverage bias.

In the sample study provided is is informed that:

The proportion of household in the community with no telephone is, 0.04.

The proportion of household in the community with cell phones is, 0.10.

The proportion of household in the community with unlisted telephone numbers is, 0.25.

On summing up these probabilities we get, 0.39 as the sum of all probabilities.

This violates the rule of sum of probabilities to be 1.

This indicating that the sampling frame does not include certain portion of the population.

Hence, causing an under coverage bias.