A builder claims that air conditioners are installed in at least 85% of all homes being constructed today in the city of Tucson, Arizona. The city of Tucson would like to test this claim and estimate the poputlation proportion of houses that have air conditioners installed. The city took a simple random sample of 86 new homes, which indicated that 81 had air conditioners installed. Test whether there is significant evidence to support the builders claim. Use a significance level of 0.01.
a) What is the parameter of interest? (include context)
b) State the null and alternative hypothesis.
c) Check the conditions of inference.
d) Calculate the test statistic, show work.
e) Give the appropriate p-value and state whether it is one-sided or two-sided.
f) Calculate the appropriate 99% confidence interval. Show work.
g) Finally, using the results from above, summarize your conclusions to the city of Tucson. Use the four part conclusion method.