Question

A real estate company, We Rent Houses, regularly conducts survey for average rents in Tampa Bay area. According to its latest survey, the sample mean rent in 2019 was $950 for Pasco County and $1,160 in Hillsborough County. Assume the survey sampled rents for 160 rental units in each county. Also, assume the standard deviation in rents based on the survey was $175 in Pasco County and $230 in Hillsborough County. Do not use PHStat4 for this part. Compute the values manually.

a. Calculate a 95% confidence interval for the population mean rent for Hillsborough County. Provide an interpretation of the confidence interval.

b. Calculate a 95% confidence interval for the population mean rent for Pasco County. Interpret.

c. Is it possible that the population mean rent in Pasco County is higher than that in Hillsborough County? Explain

Answer 1

a) The 95% confidence interval for population mean is

where

degrees of freedom = 160 -1 =159

For 95% confidence with df =159 , tc = 1.97

Thus , 95% confidence interval for population mean rent for Hillsborough county is

= (1124.18 , 1195.82 )

Interpretation

We are 95% confident that the population mean rent for Hillsborough county is contained in the interval ( $1124.18 , $1195.82 )

b) For Pasco county

degrees of freedom = 160 -1 =159

For 95% confidence with df =159 , tc = 1.97

Thus , 95% confidence interval for population mean rent for Pasco county is

= (922.75, 977.25)

Interpretation

We are 95% confident that the population mean rent for Pasco county is contained in the interval ($922.75, $977.25 )

c) No , it is not possible that population mean rent for Pasco county is higher than that in Hillsborough county.

As the upper limit of confidence interval for mean rent for Pasco county (Upper limit =977.25 ) is less than lower limit of confidence interval for Hillsborough county ( lower limit =1124.18). Thus it is not possible that population mean rent for Pasco county is higher than that in Hillsborough county.