An artide in Urban Ecosystems,\"Urbanization and warming of Phoenix (Arizona, US

Question

An artide in Urban Ecosystems,"Urbanization and warming of Phoenix (Arizona, USA): Impacts, feedbacks and mitigation," (2002, Vol. 6, pp. 183-203) mentions that Phoenix is ideal to study the effects of an urban heat island because it has grown from a population of 300,000 to approximately 3 million over the last 50 years, and this is a period with a continuous, detailed climate record. The 50 year averages of the mean annual temperatures at eight sites in Phoenix are shown below. Check the assumption of normality in the population with a probability plot. Construct a 90% confidence interval for the standard deviation over the sites of the mean annual temperatures. Round the answers to 3 decimal places. Average Mean Site Sky Harbor Airport Phoenix Greenway Phoenix Encanto Waddell Litchfield Laveen Maricopa Harlquahala Temperature 23.3 21.7 21.6 21.7 21.3 20.7 20.9 20.1 708 114.659

Explanation / Answer

CONFIDENCE INTERVAL FOR STANDARD DEVIATION
ci = (n-1) s^2 / ^2 right < ^2 < (n-1) s^2 / ^2 left
where,
s = standard deviation
^2 right = (1 - confidence level)/2
^2 left = 1 - ^2 right
n = sample size
since alpha =0.1
^2 right = (1 - confidence level)/2 = (1 - 0.9)/2 = 0.1/2 = 0.05
^2 left = 1 - ^2 right = 1 - 0.05 = 0.95
the two critical values ^2 left, ^2 right at 7 df are 14.0671 , 2.167
s.d( s^2 )=0.9441
sample size(n)=8
confidence interval for ^2= [ 7 * 0.8913/14.0671 < ^2 < 7 * 0.8913/2.167 ]
= [ 6.2393/14.0671 < ^2 < 6.2393/2.1673 ]
[ 0.4435 < ^2 < 2.8788 ]
and confidence interval for = sqrt(lower) < < sqrt(upper)
= [ sqrt (0.4435) < < sqrt(2.8788), ]
= [ 0.666 < < 1.6967 ]

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.