# If the population mean sold price is actually 650

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If the population mean “Sold Price” is actually 650 (\$000s), I would consider the interval estimate obtained in (a), to be satisfactory because the population mean lies between 547.22 and 765.18. Task 7 (a) Use Excel to produce a Descriptive Statistics table for the brick veneer properties in your sample suitable for constructing an interval estimate of the population proportion of brick veneer properties. Hence determine: Descriptive analysis for brick venner(Building Type) Mean 0.4 p Standard Error 0.07 Median 0 Mode 0 Standard Deviation 0.49 Sample Variance 0.24 Kurtosis -1.9 Skewness 0.42 Range 1 Minimum 0 Maximum 1 Sum 20 Count 50 Confidence Level(99.0%) 0.19 e i) A point estimate of the proportion of brick veneer properties in the population. Point estimate- π ≈ p = 0.4 ii) A 99% confidence interval estimate of the proportion of brick veneer properties in the population Here, e= 0.19

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p – e < µ < p + e = 0.4- 0.19 < µ < 0.4 + 0.19 =0.21 < µ < 0.59 Precision = (p+e) – (p-e) = 0.59- 0.21 = 0.38 Therefore, it can be concluded with 99 % confidence that the population properties of the Brick veneer lie between 0.21 and 0.59. b) Using the following formula : (Sample statistic) (Critical z or t) (Standard error of the sample statistic) Use the rule of thumb for good normal approximation (Slide 3 of Week 7 Session 2) for proportion, then the Empirical Rule (Slide 8 of Week 5 Session 1) for a Normal distribution to determine a 95% confidence interval estimate of the proportion of brick veneer properties in the population. Descriptive analysis for brick venner(Building Type) Mean 0.4 p Standard Error 0.0 7 Median 0 Mode 0 Standard Deviation 0.4 9 Sample Variance 0.2 4 Kurtosis -1.9 Skewness 0.4 2 Range 1 Minimum 0 Maximum 1 Sum 20 Count 50 Confidence Level(95.0%) 0.1 4 e Point of estimate = 0.4 Here, p = 0.4, e= 0.14, σ = 0.49 p ± Z α/2 √ p (1-p)/ √n =0.4 ± Z (0.025) √0.4 (1-0.4)/ √50 =0.4 ± 1.96 √0.4 * 0.6/ 7.07 =0.4 ± 0.1381 (≈ 0.084)
=0.4 ± 0.14 =p ± e Lower limit = 0.4 – 0.14 = 0.26 Upper limit = 0.4 + 0.14 = 0.54 Precision= upper limit – lower limit = 0.54 – 0.26 = 0.28 Therefore, with 95% confidence, population proportion of brick veneer properties lies Between 0.28 to 0.54 By empirical rule, = p ± 2σ = 0.4 ± 2 * 0.49 =0.4 ± 0.98 = p ± e Lower limit = 0.4 – 0.98 = -0.58 Upper limit = 0.4 + 0.98= 1.38 Therefore, by empirical rule, with 95% confidence, population proportion of brick veneer Properties lies between – 0.58 to 1.38 C) Compare in terms of the precision, the interval manually calculated in (b) with the Interval obtained from the Descriptive Statistics table in (a). Explain why the direction of the change in precision is expected.
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