Question

One measure of the state of the economy is the amount of money homeowners pay on their mortgage each month. To determine the extent of change between this year and 5 years ago, a random sample of 150 homeowners was drawn. The monthly mortgage payments for each homeowner for this year and for 5 years ago was recorded (the amounts were adjusted so that we could compare constant dollars). One would like to use the data to estimate the mean difference in monthly mortgage payments with 90% confidence.

• Which formula is appropriate for the scenario described?

  ˆp±z√ˆp(1−ˆp)np^±zp^(1-p^)n

  ¯yd±tsd√ndy¯d±tsdnd

  (¯y1−¯y2)±t√s21n1+s22n2(y¯1-y¯2)±ts12n1+s22n2

  ¯y±ts√ny¯±tsn

• Using the information below, calculate the confidence interval, rounding your limits to 3 decimal places.

	Mean	Std. Error	Critical Value
2016 - 2011	-117.868	11.022	1.655

Lower limit:

Upper limit:  

• Interpret: With 90% confidence, we estimate the Select an answer mean mortgage payment mean difference proportion of mortgage payments  in Select an answer 2011 2016  is between  and  more than that of Select an answer 2011 2016  .

Answer 1

Here we take a random sample of 150 homeowners .

We want to estimate the mean difference in monthly mortgage payments with 90% confidence.

Here we need to use the following formula to find the 90% confidence interval.

Here

t = 1.655

Lower limit =

Upper limit =

Interpret:

With 90% confidence, we estimate the Select an answer mean mortgage payment mean difference proportion of mortgage payments in Select an answer 2011- 2016 is between -136.109 to -99.627 and the mean of 2011 is more than that of the mean of 2016 .