Question

With domestic sources of building supplies running low several years ago, roughly 60,000 homes were built with imported Chinese drywall. According to an article federal investigators identified a strong association between chemicals in the drywall and electrical problems, and there is also strong evidence of respiratory difficulties due to the emission of hydrogen sulfide gas. An extensive examination of 57 homes found that 45 had such problems. Suppose these 57 were randomly sampled from the population of all homes having Chinese drywall.

(b) Calculate a lower confidence bound using a confidence level of 99% for the percentage of all such homes that have electrical/environmental problems. (Round your answer to one decimal place.)

(c) If it is actually the case that 80% of all such homes have problems, how likely is it that the test of (a) would not conclude that more than 50% do? (Round your answer to four decimal places.)

Answer 1

b)

p̂=x/n-1=45/57-1=45/56=0.80

99% of CI lower limit =p̂-2.33(p̂(1-p̂)/w)

=0.80-2.33((0.80*0.20)/56)

=0.80-0.125

=0.675~67.5%

c)

use formula of Z equation in (a)

Z=(0.80-0.50)/((0.50*0.50)/56)

      =4.49

P-value=p(Z>4.49)

=p(Z<-4.49)

=NORMSDIST(-4.49   

=0.00

Conclusion:-Reject Ho,enough evidence to conclude that the proportion is greater than 50%

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