Sampling and Statistical Inference
dinkaufa
real_estate_instructions.pptxCritical Thinking assignment
For problem #1 & 2, compute Sample Mean, i.e. xbar Median range Sample Standard Deviation for each of the 3 categories
Be sure to submit your Excel file with the work/computations.
Note : The +/- means add and subtract. For example,9 +/- 7 means 9+7 = 16 9-7= 2 The confidence interval would be [2, 16]
For problems 4 and 5, you will use formula 8.2 on page 346:
xbar +/- (t_α/2) * s/sqrt(n)
sqrt(n) means “the square root of n” xbar = sample average s= sample standard deviation degrees of freedom = n-1
α =1- confidence coefficient
For option 1:
α =1-.95 =.05 So, α/2= .05/2 = .025
For #4: degrees of freedom = n-1 = 40-1=39 For #5: degrees of freedom = n-1 = 18-1=17
To find t_α/2 = t.025 you can use table 2 on page 642-643:
Under the .025 column in that table scroll down to degrees of freedom =39 to do problem #4 and find t.025 <-------xbar +/- t.025 * s/sqrt(40)
degrees of freedom =17 to do problem #5 and find t.025 <-----xbar +/- t.025 * s/sqrt(18)
For option 2:
α =1-.90 = .1 So, α/2= .1/2 = .05 For #4 and #5: degrees of freedom = n-1 = 50-1=49
To find t_α/2 = t.05 you can use table 2 on page 642-643: Under the .05 column in that table scroll down to
degrees of freedom =49 to do problem #4 & #5 and find t.05
Use xbar +/- t.05 * s/sqrt(50)
Be sure to completely show your work with all the appropriate numbers plugged into the formula. I am very interested in the work. i.e, compute xbar, t.025 (or t.05 for option 2), s, and sqrt(n) and plug them into the formula.
You can use Excel to compute
xbar +/- (t_α/2) * s/sqrt(n)
For problem #6, you will use formula 8.3 on page 353:
n = (z_α/2)2 * s2/E2 <----------Sample size formula s = sample standard deviation for the column Use the sample standard deviation, s, that you computed in parts 1 and 2 E = the margin of error
Round up n. e.g. n=56.1 rounded up is n=57
For Option 1:
α =1-.95 =.05 So, α/2= .05/2 = .025 So the formula is: n = (z_.025)2 * s2/E2
You will use z_.025 =1.96 (see page 353 for an explanation why).
You will use E=40 and then E=15 (since the units are in thousands)
For Option 2:
α =1-.90 =.10 So, α/2= .10/2 = .05 So the formula is: n = (z_.05)2 * s2/E2
You will use z_.05 =1.65 (see 1st table on inside front book cover). (.05 is between .0495 and .0505. Choose the bigger z-value: 1.65)
You will use E=5 and then E=4
For #7:
Example: Suppose the avg. list price of cars at a lot is $20,000 and the avg. sale price is $15,000 and the mean no. of days to sell is 3 months. (AVgSalePrice)/(AvgListPrice) =15,000/20,000 = 0.75 Then one would expect a car to sell for 75% of its original list price.
e.g. If a car is listed at $25,000, then its estimated sale price is $25,000*0.75 = $18,750
Thus, you would expect the car to sell for $18,750 in about 3 months.
