Application

Now that you have completed all of the activities in this chapter, use the concepts and techniques that you've learned to respond to these questions.

  1. Scenario: We'll continue to examine the World Development Indicators data in BirthRate 2005. This time we'll see if we can use a normal model to represent one or more variables.

    1. Complete the steps necessary to create a normal quantile plot for the Fertil column. Fertil is the mean number of children that women have during their child-bearing years in each country. Report on what you see in the graph and what you conclude about the suitability of a normal model.

    2. Consider a random variable X ~ N(2.993, 1.590). Such a variable has the same mean and standard deviation as Fertil. For Fertil, 10% of observations fell below 1.319 children. What proportion of X lies to the left of 1.319?

    3. Using the same X, find Pr(X > 5.5). Compare your result to the observed data for Fertil.

    4. Find the third quartile for X and compare the result to the third quartile for Fertil.

  2. Scenario: In the first chapter we looked at Michelson's early measurements of the speed of light. The data table is Michelson 1879.

    1. Complete the steps necessary to create a shadowgram of the Velocity data. Paste a copy of the graph in your report and comment on what you see.

    2. Construct a normal quantile plot for the Velocity column. Do you think that a normal model is suitable for this variable? Explain.

    3. "Measurement error" is sometimes assumed to be normally distributed. What does this set of data suggest about that assumption?

  3. Scenario: In Chapter 2 we first looked at the Concrete data table containing experimental data. The point of the experiment was to develop concrete that has high compressive strength.

    1. Complete the steps necessary to create a normal quantile plot for the Compressive Strength column. Report on what you see in the graph and what you conclude about the suitability of a normal model.

    2. Consider a random variable X~N(35.818, 16.706). Such a variable has nearly the same mean and standard deviation as Compressive Strength. Use this normal model and find its 10th, 25th, 50th, 75th, and 90th percentiles. Compare your computed values to the observed corresponding percentiles and report what you find.

  4. Scenario: Normal models are frequently used to describe the fluctuations in stock market prices. Open the data table called Stock Index Weekly Changes. This table contains the weekly proportionate changes in six major international stock market indexes for all of 2008. In the fall of 2008, world financial markets suffered precipitous declines in value.

    1. Construct a normal quantile plot for each column in this table (except Date). Which column would you say is best described by a normal model? Explain your thinking.

    2. Which column would you say is least described by a normal model? Explain your thinking.

    3. Identify the mean and standard deviation of a normal distribution that might be suitable for modeling the HangSeng index. Use your model to estimate the percentage of weeks that the index lost value (that is, had a weekly change that was less than or equal to zero).

    4. Compare your result in the prior question to the actual percentage of weeks that the HangSeng lost value in 2008. Comment on the comparison.

  5. Scenario: In this scenario, we return to the data from the American Time Use Survey (TimeUse). Our data table contains observations from approximately 16,000 respondents in 2003 and 2007. Use the Data Filter to select and include just the 2003 responses.

    1. Complete the steps necessary to create a shadowgram of the Sleeping data (that is, time spent sleeping). Paste a copy of the graph in your report and comment on what you see.

    2. Construct a normal quantile plot for the Sleeping column. Do you think that a normal model is suitable for this variable? Explain.

    3. Repeat steps a and b for the column containing the ages of the respondents.

  6. Scenario: In this scenario, we return to the FTSE100 data table, with values of the London Stock Exchange index. We'll focus on the daily closing value of the index, the daily percentage change, and the daily volume (number of shares traded).

    1. Use the Distribution platform to summarize the daily closing values and the daily percentage change. Comment on interesting features of these two distributions.

    2. The daily percentage changes are calculated from the data in the Close column, and clearly are much better approximated by a normal model than are the daily closing figures. In fact, computing percentage changes is one strategy that analysts use to transform time series into a nearly normal variable. Construct NPPs for both Close and Change%, and report on your findings.

    3. Would a normal model be an apt description of the daily volume variable? If so, which normal model fits this variable?

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