One team member mentioned that he had read an Associated Press article recently that said about 8% of all households have only a cell phone. Greg mentioned that any estimate they came up with should have a margin of error of ±0.03, and the others at the meeting agreed. a. Assuming that the group wishes to develop a 95% confidence interval estimate, determine the required sample size if the population proportion of cell phone–only users is 8%. b. Supposing the group is unwilling to use the 8% baseline proportion and wants to have the sample size be conservatively large enough to provide a margin of error of no greater than ±0.03 with 95% confidence, determine the sample size that will be needed.
Helen Hutchins and Greg Haglund took the elevator together to the fourth-floor meeting room, where they were scheduled to meet the rest of the market research team at the Franklin Company. On the way up, Helen mentioned that she had terminated her contract for the land-line telephone in her apartment and was going to be using her cell phone exclusively to save money. “I rarely use my house phone anymore and about the only calls I get are from organizations wanting donations or doing surveys,” she said. Greg said that he and his wife were thinking about doing the same thing. As Helen and Greg walked toward the meeting room, Helen suddenly stopped. “If everyone did what I am doing, wouldn’t that affect our marketing research telephone surveys?” she asked. “I mean, when we make calls the numbers are all to land-line phones. Won’t we be missing out on some people we should be talking to when we do our surveys?” Helen continued. Greg indicated that it could be a problem if very many people were using cell phones exclusively like Helen. “Maybe we need to discuss this at the meeting today,” Greg said. When Helen and Greg brought up the subject to the market research team, several others indicated that they had been having similar concerns. It was decided that a special study was needed among the Franklin customer base to estimate the proportion of customers who were now using only a cell phone for telephone service. It was decided to randomly sample customers using personal interviews at their business outlets, but no one had any idea of how many customers they needed to interview. One team member mentioned that he had read an Associated Press article recently that said about 8% of all households have only a cell phone. Greg mentioned that any estimate they came up with should have a margin of error of ±0.03, and the others at the meeting agreed.
a. Assuming that the group wishes to develop a 95% confidence
b. Supposing the group is unwilling to use the 8% baseline proportion and wants to have the sample size be conservatively large enough to provide a margin of error of no greater than ±0.03 with 95% confidence, determine the sample size that will be needed.
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