1 A survey asked PGCC students whether they had purchased an

1.       A survey asked PGCC students whether they had purchased an e-book during the last semester. After surveying 164 students, a 95% confidence interval was found to be (0.485, 0.637). Answer the following questions based on this scenario.

a.        [1] Which one of the following statements is true concerning the meaning the 95% confidence interval? Choose one by highlighting it.

                           i.      The percentage of students in the sample who purchased an e-text was between 48.5% and 63.7%.

                          ii.      We’re 95% sure between 48.5% and 63.7% of all PGCC students purchased an e-text last semester.

                        iii.      95% of the sampled students purchased an e-text last semester.

                        iv.      We’re 95% sure that between 48.5% and 63.7% of the 164 students purchased an e-text last semester.

                          v.      Between 48.5% and 63.7% of all PGCC students purchased an e-text last semester.

b.       [1] Based on the confidence interval above can we conclude that more than half of all PGCC students purchased an e-text last semester? Explain briefly.

c.        [1] If a 90% level of confidence is used instead, will the margin of error from the same sample be larger than that produced by the 95% confidence interval above? Choose one.

Yes                          No                           Can’t be determined

[1] The margin of error was not reported. However, you can still determine what it is from the confidence interval. Give the margin of error

Solution

a)  ii.      We’re 95% sure between 48.5% and 63.7% of all PGCC students purchased an e-text last semester.

b.       [1] Based on the confidence interval above we cab conclude that more than half of all PGCC students purchased an e-text last semester. as there is proprotionof lower limit cof confidence leve is near to 0.5 and it upper confidence limit is far away from 0.5 so the it is expected that half of all PGCC students purchased an e-text last semester.

c.        [1] If a 90% level of confidence is used instead, will the margin of error from the same sample be larger than that produced by the 95% confidence interval above?  

No