You ask your neighbor to water a sickly plant while you are on vacation.
Without water it will die with probability 0.8; with water it will die with
probability 0.15. You are 90 percent certain that your neighbor will
remember to water the plant.
(a) What is the probability that the plant will be alive when you return?
(10%)
(b) If it is dead, what is the probability your neighbor forgot to water it?
(10%)
Many public polling agencies conduct surveys to determine the current
consumer sentiment concerning the state of the economy. For example, the
Bureau of Economic and Business Research (BEBR) at the University of
Florida conducts quarterly surveys to gauge consumer sentiment in the
Sunshine State. Suppose that BEBR randomly samples 484 consumers and
finds that 257 are optimistic about the state of the economy. (Use
Z0.05 = 1.645 , Z0.1 = 1.28 )
(a) Use a 90% confidence interval to estimate the proportion of all
consumers in Florida who are optimistic about the state of the economy?
(10%)
(b) Based on the confidence interval, can BEBR infer that the majority of
Florida consumers are optimistic about the economy? (10%)
A state employee wishes to see there is a significant difference in the
number of employees at the interchanges of three state toll roads. The data
are shown in Table 1.
Many variables influence the sales of existing single-family homes. One of
these is the interest rate charged for mortgage loans. A SAS printout of the
simple linear regression is provided in Table 2.
(a) Do the data provide sufficient evidence to indicate that the mortgage
interest rate contribute information for the prediction of annual sales of
existing single-family homes? (Use α = 0.05 ) (10%)
(b) Compute R-Squared and interpret its value. (10%)
(c) A 95% confidence interval for the mean annual number of existing
single-family homes sold is [3714.7, 4052] when the average annual
mortgage interest rate is 8.0%, and a 95% prediction interval for the
annual number of existing single-family homes sold is [3364.1, 4402.7]
when the average annual mortgage interest rate is 8.0%. Explain why
the widths of intervals found in confidence interval and prediction
interval differ. (10%)
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