A random sample of 22 restaurants was selected, and the temperature of the coffe

Question

A random sample of 22 restaurants was selected, and the temperature of the coffee sold at each was measured. The sample mean temperatures was 161.9F with a sample standard deviation of 10.2F. Construct a 90% confidence interval estimate for the value of the population mean temperature of coffee sold at all restaurants. Assume the temperatures are approximately normally distributed. (Show all steps for the confidence interval below, including writing a sentence that correctly interprets the confidence interval; express answer to three decimal places.)

Explanation / Answer

Mean is 161.9 and s is 10.2

for sample size of 22, the standard error SE is s/sqrt(N)=10.2/sqrt(22)=2.17465

z for 90% confidence is 1.65

thus lower bound is mean-z*SE=161.9-1.65*2.17465=158.312

upper bound is mean+z*SE=161.9+1.65*2.17465=165.488

thus we are 905 confident that the true population mean temperature of coffee sold at all restaurants falls in above range

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