Question

A Statistics major student, wants to estimate the true proportion of the Minnesotans (between ages 22 and 35) using Metro Transit. He surveys randomly selected 200 Minnesotans between the ages of 22 and 35 and finds that 62% of them use Metro Transit.

A. What is the population and what is the measurement we are interested in?

B. What proportion is the 62% mentioned in the problem? (sample/population?)

C.Construct the 95% confidence interval to estimate the true proportion of Minnesotans using Metro Transit between the ages of 22 and 35. Show your work.(all the steps)

D.

If we used the same procedure as in Question 12 but instead calculated a 90% confidence interval

Group of answer choices

90% confidence interval would be wider than 95%.

90% confidence interval would be smaller than 95%.

90% confidence interval would remain the same as in Question 12.

None of the above

E.If we hypothesize that more than half the population in Minnesota use the Metro Transit would our hypothesis be true and why? (Use the 95% confidence interval from Question

F.

If we instead had a sample size of 500 Minnesotans,

Group of answer choices

95% confidence interval would be wider for bigger sample size of 500.

95% confidence interval would be smaller for bigger sample size of 500.

95% confidence interval would remain the same as in Question 12.

None of the above

Answer 1

A. Population : The total population (no of people) in Minnesota between ages 22 and 35

Measurement : The proporiton of population in Minnesotans between ages 22 and 35 using Metro Transit.

B. 62% is sample proportion. ( )

C. Confidence interval = CI

n = 200

z value for 95% CI = 1.960

= 0.62

CI = 0.62 +/- 0.067

CI = 0.553 , 0.687

D. 90% CI

z value for 90% CI = 1.645

Hence ME of reduce and CI range will also reduce.

90% confidence interval would be smaller than 95%.

E. p = 0.50

CI range for 95% CI = 0.553 , 0.687

As 0.50 does not fall in the CI range, we reject the Null hypothesis.

F. IF the sample size increases, ME will reduce, hence CI range will also reduce.

95% confidence interval would be smaller for bigger sample size of 500.