Question

1.              A leading consumer magazine, The False Traders, claims that the small coffee sold at PHILZ coffee shop does not contain 12 ounces of coffee. A sample of 16 customers who purchased a small coffee yielded the following information:

- a sample mean equal to 11.90 ounces and a sample standard deviation of 0.16 ounces.

a. Set up a 90% confidence interval for the true population mean?

b. At the 5% level, test the hypothesis whether the true mean is less than 12 ounces.

Answer 1

Solution -

A. Set up a 90% confidence interval for the true population mean?

Alpha level=100-90=10%=0.1/2=0.05Degrees of freedom= 16-1=15T-value=1.753Standard error= 0.16/16^0.5=0.04This implies that = 11.90-(1.753*0.04), 11.90+ (1.753*0.04)We are 90% confident that the true population mean lies between 11.82988 & 11.97012

B. At the 5% level, test the hypothesis whether the true mean is less than12 ounces.

H0: ?=12H1: ?<12Alpha level= 5%= 0.05Z score= -1.645Z= (11.90-12)/ [0.16/ (16) ^0.5] = -2.5Since the Z score= -1.645 is greater than -2.5 the null hypothesis is rejected. This implies that the true mean is less than 12 ounces

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