Question

The following data are monthly rents (in dollars) of studio and one-bedroom apartments in Harrisburg, Pennsylvania, in 2007, obtained from a random sample of such apartments advertised at rent.com in July 2007:

500, 549, 569, 575, 585, 600, 630, 680, 705, 790, 845
The mean of these eleven rent prices is $638.91 ,and the standard deviation is $105.93 .
1. Determine the standard error of the sample mean.
2. Describe what the population mean µmeans in this context.
3. Determine a 95% confidence interval for µ.
4. Write a sentence interpreting what this interval means.
5. Would you expect about 95% of the studio and one-bedroom apartments in Harrisburg in July 2007 to have a rent price within this interval? Explain.

Answer 1

Part 1

SE= 31.94

Part2;

The population mean tells us that what would be the mean of all the monthly rents (in dollars) of studio and one-bedroom apartments in Harrisburg, Pennsylvania, in 2007.

Part 3:

576.31, 701.51

Part4:

This means that the 95%of the interval 576.31, 701.51 will have contain the value of the population parameter mean u.

Part 5:

Yes. out of 100 , 95 of the intervals will contain the true value of population mean u .

Explanation:

Part 1

The standard error is calculated using the formula

SE = S/√n

where s is the standard deviation of the sample = $ 105.93

and n is the sample size= 11

Putting the values we get

SE= $ 105.93/ √11= 31.939

Part2;

The population mean tells us that what would be the mean of all the monthly rents (in dollars) of studio and one-bedroom apartments in Harrisburg, Pennsylvania, in 2007.

Part 3:

The z∝/2 value for 0.05 is ± 1.96

The 95 % confidence interval will be given by

x` ±z ∝/2 * s/√n

Putting the values

638.91 ± 1.96 * 31.94

638.91 ± 62.6006

576.31, 701.51

Part4:

This means that the 95%of the interval 576.31, 701.51 will have contain the value of the population parameter mean u.

Part 5:

Yes when the hypothesis testing is done and the sample mean is found to be equal to the population mean then it means that the population mean is to be found in this interval; 95% .

Or out of 100 , 95 of the intervals will contain the true value of population mean u.