Question

This is Question 2:

Price Sold	Zestimate	Higher/Lower	Percentage
$225,000	$254,514	$29517 - L	-0.116
$302,000	$315,797	$13797 - L	-0.044
$184,900	$182,583	$2317 - H	0.013
$250,000	$237,607	$12393 - H	0.052
$200,500	$200,545	$45 - L	-0.0002
$277,000	$183,000	$94000 - H	0.514
$229,900	$233,615	$3715 - L	-0.016
$263,250	$255,286	$7964 - H	0.031
$187,500	$186,726	$774 - H	0.004
$148,340	$146,843	$1497 - H	0.01
$231,000	$234,549	$3549 - L	-0.015
$157,055	$197,534	$40479 - L	-0.205
$139,900	$120,992	$18908 - H	0.156
$183,500	$185,936	$2436 - L	-0.013
$340,000	$348,212	$8212 - L	-0.024
$231,750	$232,079	$329 - L	-0.001
$347,500	$348,557	$1057 - L	-0.003
$342,150	$340,700	$1450 - H	0.004
$499,000	$482,415	$16585 - H	0.034
$377,500	$372,025	$5475 - H	0.015
$175,500	$177,108	$1608 - L	-0.009
$415,000	$419,435	$4435 - L	-0.011
$274,900	$268,667	$6233 - H	0.023
$248,800	$288,288	$39488 - L	-0.137
$224,900	$189,330	$35570 - H	0.188
$199,900	$200,750	$850 - L	-0.004
$239,900	$241,938	$2038 - L	-0.008
$245,750	$261,476	$15726 - L	-0.06
$278,000	$279,381	$1381 - L	-0.005
$405,000	$404,156	$844 - H	0.002
$230,000	$220,563	$9437 - H	0.043

Determine a 90%, 95% and 99% confidence interval for percentage difference in “Zestimate” and selling price from question two. Interpret the intervals and explain why each of your intervals are different (which are wider and why?).

Answer 1

90 % confidence interval

	Percentage
Sample Size	31
Sample Mean	0.0134774
Standard Deviation	0.1165194
Confidence Coefficient	0.9
Significant level	0.1
Margin of error	0.03
Point Estimate	0.0134774
Lower Limit	-0.02
Upper Limit	0.05

90 % confidence interval is ( -0.02, 0.05)

95 % confidence interval

	Percentage
Sample Size	31
Sample Mean	0.0134774
Standard Deviation	0.1165194
Confidence Coefficient	0.95
Significant level	0.05
Margin of error	0.04
Point Estimate	0.0134774
Lower Limit	-0.03
Upper Limit	0.05

95 % confidence interval (-0.03,0.05)

99% confidence in terval

	Percentage
Sample Size	31
Sample Mean	0.0134774
Standard Deviation	0.1165194
Confidence Coefficient	0.99
Significant level	0.01
Margin of error	0.05
Point Estimate	0.0134774
Lower Limit	-0.04
Upper Limit	0.07

99% confidence interval is (-0.04,0.07)

each of the interval is different because MArgin of error will be decideing the lower and upper limit interval for each confidence level.

Margin of error will be calculated based on the significance level (i.e 1-confidence coefficient), standard deviation and sample size. so if we change confidence coefficient value as 90 %,95% and 99% then according to the value of margin of error will change and give different lower and upper limit intervals.

90% - (-0.02,0.05)

95% - (-0.03,0.05)

99% - (-0.04,0.07)

99% cofidence interval lloks wider than 90% and 95 % becuase upper limit value is higher than the other two intervals

Margin of error formula =confidence(significant level,standard deviation,sample size)