Question

Collect the DataCheck the Real Estate section in your local newspaper. Record the sale prices for 35 randomly selected homes recently listed in the county.

NOTE

Many newspapers list them only one day per week. Also, we will assume that homes come up for sale randomly.

1. 588777
   654345
   679231
   514567
   589876
   456342
   576567
   543786
   680364
   324176
   578354
   348729
   745368
   635478
   736453
   491847
   764836
   734629
   438274
   645274
   364846
   456739
   873937
   645278
   573847
   745636
   736547
   836474
   254637
   746473
   543729
   562437
   638746
   769373
   738392

   Table 8.5

Describe the Data'

1. Compute the following:

   1. x¯ = 606124.6857

   2. sx = 149131.0695

   3. n = 35

1. In words, define the random variable ?⎯⎯⎯X¯
2. State the estimated distribution to use. Use both words and symbols.

Find the Confidence Interval

1. Calculate the confidence interval and the error bound.
   1. Confidence Interval: _____
   2. Error Bound: _____
2. How much area is in both tails (combined)? α = _____
3. How much area is in each tail? ?2α2 = _____
4. Fill in the blanks on the graph with the area in each section. Then, fill in the number line with the upper and lower limits of the confidence interval and the sample mean.

   Figure 8.6

5. Some students think that a 90% confidence interval contains 90% of the data. Use the list of data on the first page and count how many of the data values lie within the confidence interval. What percent is this? Is this percent close to 90%? Explain why this percent should or should not be close to 90%.

Describe the Confidence Interval

1. In two to three complete sentences, explain what a confidence interval means (in general), as if you were talking to someone who has not taken statistics.
2. In one to two complete sentences, explain what this confidence interval means for this particular study.

Use the Data to Construct Confidence Intervals

1. Using the given information, construct a confidence interval for each confidence level given.

   Confidence level	EBM/Error Bound	Confidence Interval
   50%
   80%
   95%
   99%

   Table 8.6

2. What happens to the EBM as the confidence level increases? Does the width of the confidence interval increase or decrease? Explain why this happens.

Answer 1

90% CI: (563500.3, 648749.1), where, t_0.05,34=1.6909 (R code: round(qt(1-0.05,34),4))

Error bound=42624.4

No. of observations which lie in (563500.3, 648749.1)=9.

Percentage of observations which lie in (563500.3, 648749.1)=(9/35)*100=26%

Bcause 90% of CI for population mean means we are 90% confident that true mean lies in that interval and this is does not mean almost 90% of observations fall within this interval.

The CI is a range of values that is likely to include a population mean with a certain degree of confidence. Here we 90% confident that true mean lies in (563500.3, 648749.1).

Confidence level	Error bound	CI
50%	17185.99	(588938.7, 623310.7)
80%	32945.31	(573179.4, 639070.0)
95%	51228.31	(554896.4, 657353.0)
99%	68776.69	(537348.0, 674901.4)