4.170 Change in Stock Prices. Standard & Poor's maintainsone of the most widely followed indices of large-cap Americanstocks: the S&P 500. The index includes stocks of 500 companiesin industries in the US economy. A random sample of 50 of thesecompanies was selected, and the change in the price of the stock(in dollars) over the 5-day period from August 2 to 6, 2010 wasrecorded for each company in the sample. The data are available inStockChanges.

a. Use StatKey to calculate a 95% confidence interval for themean change in all S&P stock prices over these dates using thebootstrap percentiles method. Include a screen shot of your Statkeyoutput with your homework submission, and write the confidenceinterval below.

b. Use only the confidence interval you created (do not find ap-value) to predict the results of a hypothesis test to see if themean change for all S&P 500 stocks over this period isdifferent from zero.

i. Define the parameter.

ii. State the hypotheses.

iii. What significance level are you able to use based on theconfidence interval?

iv. State the conclusion using nontechnical language.

c. If any error were to occur in the decision to reject or failto reject, would it be a Type I error or a Type II error?

d. Explain what an error of this type would mean in context.

SPChange
0.29
-0.06
0.34
0.7
0.42
0.22
0.12
0.03
-0.5
0.36
0.03
0.09
-0.12
0.03
-0.47
-3.27
0.35
-0.06
0.01
0.6
0.12
4.86
-0.77
-0.03
0.39
0.1
-0.12
0.47
-0.05
0.06
-0.03
0.15
0.31
-0.15
0.32
-2.66
0.22
-0.03
0.09
0.29
0.16
0.38
0.1
0.21
0.09
0.33
0.18
1.93
0.14
0.03