Random samples of monthly rent prices, in dollars, for studio and one-bedroom ap
ID: 3126033 • Letter: R
Question
Random samples of monthly rent prices, in dollars, for studio and one-bedroom apartments, were obtained for the Pennsylvania cities of Harrisburg and Philadelphia in July 2007. A 95% confidence interval for the difference in population means µH - µP turns out to be
( -$161.1, -$22.3 ).
1. Write a sentence or two interpreting what this interval reveals about the average difference between rents in Harrisburg and Philadelphia.
2. Determine the midpoint of this interval.
3. Determine the half-width of this interval.
4. Comment on how the interval would change (both its midpoint and half-width) if you were instead to calculate a 99% CI for µH - µP.
5. Comment on how the interval would change (both its midpoint and half-width) if you were instead to calculate a 95% CI for µP - µH. (Notice that the order of subtraction has changed here.)
Explanation / Answer
Random samples of monthly rent prices, in dollars, for studio and one-bedroom apartments, were obtained for the Pennsylvania cities of Harrisburg and Philadelphia in July 2007. A 95% confidence interval for the difference in population means µH - µP turns out to be
( -$161.1, -$22.3 ).
1. Write a sentence or two interpreting what this interval reveals about the average difference between rents in Harrisburg and Philadelphia.
We are 95% confident that average difference between all rents in Harrisburg and Philadelphia will falls in the interval ( -$161.1, -$22.3 ).
2. Determine the midpoint of this interval.
Mid point =(-161.1+(-22.3))/2 = -91.7
3. Determine the half-width of this interval.
(-22.3)-(-91.7) = 69.4
4. Comment on how the interval would change (both its midpoint and half-width) if you were instead to calculate a 99% CI for µH - µP.
Mid point remains the same -91.7
Half width will increase.
5. Comment on how the interval would change (both its midpoint and half-width) if you were instead to calculate a 95% CI for µP - µH. (Notice that the order of subtraction has changed here.)
Mid point is 91.7 ( it is positive value, the sign is changed))
Half width remains the same (69.4).
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