Question

3. 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 large coffee yielded the following information:

- a sample mean equal to 11.4 ounces and a sample standard deviation of 0.16 ounces.

a. What formula would you use to set up a 90% confidence interval for the true population mean?

b. What t-value would you use to set up a 90% confidence interval for the true population mean?

(10)     b.  At the 10% level, test the hypothesis whether the true mean is less than 12 ounces.

Answer 1

(a) CI = sample mean +/- E

Assuming that the data is normally distributed, also as the population sd is not given we will use t statistics.

Formula for CI

(b) t value for 90% of confidence interval at 15 df is TINV(0.1,15) = 1.753

E = 0.070

CI = (11.33 , 11.47)

(c)

Step 1:

Ho: = 12

Ha: < 12

Step 2: test statistics

t = -15

t critical for df = 15, and level of significance = 0.10 is -1.341

As the t stat (-15) falls in the rejection area, we reject the Null hypothesis.

Also based on the CI = (11.33 , 11.47), as 12 is not in the range, we reject the Null hypothesis.

Hence, we have sufficient evidence to belive that true mean is less than 12 ounces.