You want to rent an unfurnished one-bedroom apartment in boston next year. the mean monthly rent for a random sample of 10 apartments advertised in the local newspaper is $2534. assume that the standard deviation is $670. find the 90%, 95%, and 99% confidence intervals for the mean monthly rent for this category of apartments. look at the 95% confidence interval and say whether the following statement is true or false. "this interval describes the price of 95% of the rents of all the unfurnished one-bedroom apartments in the boston area." be sure to explain your answer.

90% confidence interval: (2186.53;2881.47)

95% confidence interval: (2118.73;2949.27)

99% confidence interval: (1987.37;3080.63)

For the last part is not the best way say : "This interval describes the price of 95% of the rents of all the unfurnished one-bedroom apartments in the Boston area."

The best interpretation is this one: "We are 95% confident that the actual mean for the rents of unfurnished one-bedroom apartments in the Boston area is between (2118.73;2949.27)"

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

represent the sample mean  

population mean (variable of interest)

represent the population standard deviation

n=10 represent the sample size  

90% confidence interval

The confidence interval for the mean is given by the following formula:

  (1)

Since the Confidence is 0.90 or 90%, the value of and , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that

Now we have everything in order to replace into formula (1):

So on this case the 90% confidence interval would be given by (2186.53;2881.47)

95% confidence interval

The confidence interval for the mean is given by the following formula:

  (1)

Since the Confidence is 0.95 or 95%, the value of and , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that

Now we have everything in order to replace into formula (1):

So on this case the 95% confidence interval would be given by (2118.73;2949.27)

99% confidence interval

The confidence interval for the mean is given by the following formula:

  (1)

Since the Confidence is 0.99 or 99%, the value of and , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that

Now we have everything in order to replace into formula (1):

So on this case the 99% confidence interval would be given by (1987.37;3080.63)

For the last part is not the best way say : "This interval describes the price of 95% of the rents of all the unfurnished one-bedroom apartments in the Boston area."

The best interpretation is this one: "We are 95% confident that the actual mean for the rents of unfurnished one-bedroom apartments in the Boston area is between (2118.73;2949.27)"

(-1,-0.5)

step-by-step explanation:

step-by-step explanation:

first you will have to convert 3/4 into a decimal

which is .75

then you will have to divide 1.5 by .75

which is 2

no you have to divide