Statistics: Variance and Vanguard Total Stock

Statistics Midterm paper
Identify the implied population in the information here. Government agencies carefully monitor water quality and its effect on wetlands. Of particular concern is the concentration of nitrogen in water draining from fertilized lands. Too much nitrogen can kill fish and wildlife. Twenty-eight samples of water were taken at random from a lake. The nitrogen concentration (milligrams of nitrogen per liter of water) was determined for each sample.
1. The variable in this information is nitrogen concentration (mg nitrogen/l water).

a. number of fish
b. samples of water taken at random
c. the wetlands d. nitrogen concentration (mg nitrogen/l water) in the entire lake
e. government agencies

2. Find the technique for gathering data in the study below. A study of all-league football scores attained through touchdowns and field goals was conducted by the National Football League to determine whether field goals account for more scoring events than touchdowns (USA Today).

a. sampling
b. census
c. experiment
d. simulation
e. observational study.

3. It’s not an easy life, but it’s a good life. Suppose you decide to take the summer off and sign on as a deckhand for a commercial fishing boat in Alaska that specializes in deep-water fishing for groundfish. What kind of fish can you expect to catch? One way to answer this question is to examine the reports on groundfish caught in the Gulf of Alaska. The following list indicates the types of fish caught annually in thousands of metric tons:

a. Flatfish, 36. 3;
b. Pacific cod, 68. 6
c. sablefish, 16. 0;
d. Walleye Pollock, 71. 2;
e. Rockfish, 18. 9.

Make a Pareto chart showing the annual harvest for commercial fishing in the Gulf of Alaska.
4. How hot does it get in Death Valley? Assume that the following data are taken from a study conducted by the National Park System, of which Death Valley is a unit. The ground temperatures were taken from May to November near Furnace Creek. Compute the mode for these ground temperatures.
147 153 167 174 182 178 179 182 178 178 167 0 153 144

a. 144
b. 182
c. 167
d. 153
e. 178

5. Find the sample variance s2 for the following sample data. Round your answer to the nearest hundredth. x: 23 17 12 35 29

a. 84. 20
b. 67. 36
c. 101. 00
d. 88. 84
e. 126. 25

6. Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing an annual percent return for the Vanguard Total Stock Index (all Stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond). For the past several years, assume the following data.
Compute. x: 14 0 36 23 33 25 26 14 14 23 y: 6 5 26 17 24 17 17 5 6 6

a. 4607
b. 4803
c. 5332
d. 4243
e. 4940

Answers:
Question 1: The population is d. – the nitrogen population in the entire lake.
Question 2: The technique is a census since all events are to be measured.
Question 3: The Pareto Chart
Question 4: The mode is the most frequently occurring value in a set of data so here the mode is 178 so the answer is e.
Question 5: The sample variance is 84. 20 so the answer is a.
Question 6: The mean return for the Vanguard Total Stock Index is 20. 8 while the mean return for the Vanguard Balanced Index is 12. 9 (with bonds). Based on this data you would conclude that bonds do not reduce the overall risk of an investment portfolio since the mean return was actually less when the portfolio has bonds in it.