Question

A report concluded that the​ 33% of 1057 youth they surveyed who responded that they plan to start their own business was the highest in the region. They conducted a variety of face to face and phone interviews with youth during their survey. They noted that the margin of error was between 6.6 and 7.8 percentage​ points, and that​ "in addition to sampling​ error, question wording and practical difficulties in conducting surveys can introduce error or bias into the findings of public opinion​ polls."

Does their margin of error suggest that this was a simple random​ sample? Explain.

A.No, the margin of error from a simple random sample at​ 99% confidence would be

nothing __%, which is significantly more than the given margin or error. It is likely that a more complicated sampling method was employed.

​(Round to one decimal place as​ needed.)

B.,Yes, the data suggest that this was a simple random sample.

C. No, the margin of error from a simple random sample at​ 99% confidence would be

nothing __%, which is significantly less than the given margin or error. It is likely that a more complicated sampling method was employed.

​(Round to one decimal place as​ needed.)

Answer 1

proportion p = 33/100 = 0.33

z critical for 99% interval is 2.576 [From z critical table]

sample size n= 1057

Hence, option C

No, the margin of error from a simple random sample at​ 99% confidence would be 3.7 %, which is significantly less than the given margin or error. It is likely that a more complicated sampling method was employed.