Question

The Rails to Trails program refers to the conversion of old rail corridors into multipurpose trails for recreation and transportation. Researchers were interested in obtaining information on characteristics of users and nonusers of a 10 ‑mile‑long paved greenway trail in Greenville, South Carolina, that connects residential areas to both a university campus and the commercial downtown area of the city.

Random digit dialing of residential numbers was done using a database of exchanges. A total of 2461 persons were contacted, of which 726 completed the survey. When a household was reached, surveyors asked to speak to the adult over 18 with the next birthday. No cell phone numbers were included in the sample. In the sample, although 726 completed the survey, only 689 of these respondents provided data on their ages. Among the 689 respondents who provided data on their ages, 253 were over 65 years old.

(Part a) According to U.S. census data, 13% of the population of adults in Greenville County are over 65 years old. If the 689 completed surveys that included age data are an SRS of adult Greenville County residents, do you feel that the difference between the proportion of those over 65 that completed the survey and the population proportion of 13% can be easily explained by chance variation?

Select the correct hypotheses, ? ‑value, and conclusion in the context of the problem.

(A.) ?0:?1=?2 and ??:?1≠?2 , where ?1 is the proportion of seniors in all of Greenville County and ?2 is the proportion of seniors in the sample.

?≈0.0000 .

This is significant evidence that the sample does not represent the population of Greenville in terms of age.

(B.) ?0:?=0.13 and ??:?>0.13 .

?≈0.0000 .

This is not enough evidence that the sample represents the population of Greenville in terms of age.

(C.) ?0:?=0.13 and ??:?≠0.13 .

?≈1.0000 .

This is not enough evidence that the sample represents the population of Greenville in terms of age.

(D.) ?0:?=0.13 and ??:?≠0.13 .

?≈0.0000 .

This is significant evidence that the sample does not represent the population of Greenville in terms of age.

(Part b) Among the 726 surveys that are returned, 24.9% of respondents have used the trail in the last six months. If those under 65 are more likely to use the trail, what would be the likely direction of the bias in using 24.9% as the estimate of the proportion of all Greenville County residents who have used the trail in the last six months?

(A.) The direction of bias would be such that 24.9% underestimates the actual percent of Greenville adult residents who use the trail, since younger adults who use the trail more often were underestimated in the sample.

(B.) The direction of bias would be such that 24.9% overestimates the actual percent of Greenville adult residents who use the trail, since younger adults who use the trail more often were overestimated in the sample.

(C.) The direction of bias would be such that 24.9% overestimates the actual percent of Greenville adult residents who use the trail, since younger adults who use the trail less often were overestimated in the sample.

(D.) The direction of bias would be such that 24.9% underestimates the actual percent of Greenville adult residents who use the trail, since younger adults who use the trail less often were underestimated in the sample.

Answer 1

Part a) ANSWER IS D

Ho: P=0.13 vs. H1: P =! (not equal)0.13

This is significant evidence that the sample does not represent the population of Greenville in terms of age.

Part b)Answer is A)