You are interested in the average dollar amount of transactions at your local ph

Question

You are interested in the average dollar amount of transactions at your local pharmacy. Suppose you were able to collect a random sample of only 3 transactions: 4.50 10.00 17.50 a) Calculate by hand (not using R) a 95% confidence interval for the true population average, showing all your work. You may use R only to get t_0.025 from the qt function. b) Construct a 90% confidence interval for the true population average. c) Construct an upper bound 95% confidence interval for the true population average. d) Construct a lower bound 95% confidence interval for the true population average. e) Now use R to check whether the assumption of normality is violated (show a plot).

Explanation / Answer

A sample of only 3 transactions so dF = 2 so t0.025 = 4.303

Mean of the sample xbar = 10.67 and s =6.5255

so 95 % confidence interval = Xbar + - 4.303 * (6.5255)/sqrt(3) = (-5.5415, 26.8815)

(b) 90% confidecne inteval so t0.5 = 2.92

so 95 % confidence interval = Xbar + - 2.92 * (6.5255)/sqrt(3) = (-0.3311, 21.6711)

(c) Upper bound 95% confidence interval are the bounded only on upper side or say on poitive side of population mean so

The upper bound 95% confidence interval is calculated by t 0.05 = 2.920

Upper end point = 10.67 + 2.92 * (6.5255/sqrt(3) = 21.67

(d) Lower bound 95% confidence interval are the bounded only on Lower side or say on Negative side of population mean so

The upper bound 95% confidence interval is calculated by t 0.05 = 2.920

Upper end point = 10.67 - 2.92 * (6.5255/sqrt(3) = -0.33

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