Investment Returns:These data are the annual returns of 80 dividend stocks for the years 2005 and 2010.
(i) Produce a histogram of the 2005 returns with 7 classes.
(ii) Repeat part (i) for the 2010 returns, using the same classes in (i).
(iii) Find the mean, median, range and standard deviation for the 2005 returns.
(iv) Repeat part (iii) for the 2010 returns.
(v) Compare the performance and risk of investment among the two periods.
Question 2. (Statistical Inferences: Single Population; 2 + 6 = 8 marks)
Feasibility Study: Companies that sell groceries over the Internet are called e-grocers. Customers enter their orders, pay by credit card and receive delivery by truck. To determine whether an e-grocery would be profitable in one large city, a potential e-grocer offered the service and recorded the size of the order for a random sample of customers. The data are stored in the data file.
(i) Estimate with 99% confidence the average order in the city.
(ii) Financial analysis indicates that to be profitable the average order would have to exceed $50. Can we infer from the data that an e-grocery will be profitable in the city? Test using α = 0.01.
Question 3. (Statistical Inferences: Two Populations; 7 marks)
Safe Driving: Recent studies seem to indicate that using a mobile phone while driving is dangerous. One reason for this is that a driver’s reaction times may slow while he or she is talking on the phone. Researchers measured the reaction times of 143 drivers who owned a mobile phone, 78 drivers on the phone and 65 drivers not on the phone. The reaction times were recorded (in seconds). Can we conclude that the reaction times are slower for drivers using mobile phones? Test using α = 0.05.
Question 4. (Statistical Inferences: Two Populations; 7 marks)
To sell or not to sell: The fluctuations in the stock market induce some investors to sell and move their money into more stable investments. To determine the degree to which recent fluctuation affected ownership, a random sample of 150 people who confirmed that they owned some shares were surveyed. The values of the holdings were recorded at the end of last year and at the end of the year before. Can we infer that the average value of the shareholdings has changed? Test using α = 0.10.