Standard & Poor€™s maintains one of the most widely followed indices of large-cap American stocks: the S&P 500. The index includes stocks of 500 companies in industries in the US economy. A random sample of 50 of these companies was selected, and the change in the price of the stock (in dollars) over the 5-day period from August 2 to 6, 2010 was recorded for each company in the sample. The data are available in Stock Changes.

(a) Is this an experiment or an observational study? How was randomization used in the study, if at all? Do you believe the method of data collection introduced any bias?

(b) Describe one way to select a random sample of size 50 from a population of 500 stocks.

(c) Figure 4.35 shows a boxplot of the data. Describe what this plot shows about the distribution of stock price changes in this sample.

Figure 4.35

(d) Give relevant summary statistics to describe the distribution of stock price changes numerically.

(e) Use StatKey or other technology to calculate a 95% confidence interval for the mean change in all S&P stock prices. Clearly interpret the result in context.

(f) Use the confidence interval from part (e) to predict the results of a hypothesis test to see if the mean change for all S&P 500 stocks over this period is different from zero. State the hypotheses and significance level you use and state the conclusion.

(g) Now give the null and alternative hypotheses in a test to see if the average 5-day change is positive. Use StatKey or other technology to find a p-value of the test and clearly state the conclusion.

(h) If you made an error in your decision in part (g), would it be a Type I error or a Type II error? Can you think of a way to actually find out if this error occurred?

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