Most of the stock trades at an office that handles over-the-counter retail stock sales are fairly small, but sometimes a big trade comes through. These data show the dollar value of a sample of 11 trades made during the previous day.
+1,500, +1,000, +1,000, +500, +750, +850, +1,800, +1,250, +15,500, +1,750, +2,250
(a) Using a normal quantile plot, determine whether these data might be a sample from a normally distributed population.
(b) On the basis of the skewness and kurtosis of this sample, how large a sample does the CLT condi- tion require in order to rely on a t-interval for the mean?
(c) Assuming that the data are nearly normal, find the 95% one-sample t-interval for the mean. What does it mean that the interval includes zero?
(d) How does the 95% interval change if the largest data point is excluded?
(e) Explain why the lower endpoint of the 95% confidence interval is positive after the outlier is removed, although it is negative with the outlier.