3. Scott wants to estimate the cost of a night at a Los Angeleshotel. He called

Question

3. Scott wants to estimate the cost of a night at a Los Angeleshotel. He called a
random sample of 8 hotels and got a sample mean cost for one nightof $145
with sample standard deviation $40.
(a) Find an 85% confidence interval for the population meancost.
(b) What size sample does he need to say with 90% confidencethat the sample
mean is within $10 of the population mean?

Explanation / Answer

Given n=8, xbar=145, s=40 (a) Find an 85% confidence interval for the population meancost. =0.15, Z(0.075)=1.44 (check normal table) The 85% CI is xbar ± Z*s/n --> 145 ± 1.44*40/sqrt(8) --> (124.64, 165.36) (b) What size sample does he need to say with 90% confidencethat the sample mean is within $10 of the population mean? =0.1, Z(0.05)=1.645 (check normal table) E=10 n=(Z*s/E)^2 = (1.645*40/10)^2 =43.29 Take n=44

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