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Putting It Together: Psychological Profiles Researchers wanted to determine if the psychological profile of healthy children was different than for children suffering from recurrent abdominal pain (RAP) or recurring headaches. A total of 210 children and adolescents were studied and their psychological profiles were graded according to the Child Behavior Checklist 4–18 (CBCL). Children were stratified in two age groups: 4 to 11 years and 12 to 18 years. The results of the study are summarized in the following table:

(a) Compute the sample standard deviations for each group.

(b) What sampling method was used for each treatment group? Why?

(c) Use a two sample -test for independent samples to determine if there is a significant difference in mean CBCL scores between the control group and the RAP group (assume that both samples are simple random samples).

(d) Is it necessary to check the normality assumption to answer part (c)? Explain.

(e) Use the one-way ANOVA procedure with  to determine if the mean CBCL scores are different for the three treatment groups.

(f) Based on your results from parts (c) and (e), can you determine if there is a significant difference between the mean scores of the RAP group and the headache group? Explain.

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Roosevelt versus Landon One of the most famous presidential elections (from a statistician’s point of view) is the 1936 contest between incumbent Franklin D. Roosevelt (FDR) and Republican challenger Alf Landon. The notoriety of the election comes from the fact that polling done by Literary Digest suggested that Landon would win by a 3 to 2 margin. However, Roosevelt actually crushed Landon in the general election.
After the election, author and editor David Lawrence studied the vote. Lawrence asked the following question: “To what extent was the campaign a reflection of a new trend in American politics, a trend in which the federal government’s paternalistic interest in the citizen brought an amazing reward to the party in power?”
As part of FDR’s New Deal policies to help get the United States out of the Great Depression, the federal government created the Agricultural Adjustment Administration (AAA). The AAA tried to force higher prices for commodities by paying farmers not to farm and not to bring cattle to market.
To determine whether farm subsidies may have played a role in the election results, Lawrence looked at election results in 2052 counties. He segmented the counties based on AAA funding between 1934 and 1935 as follows:

• High-funded AAA counties received $500,000 or more in AAA money

• Medium-funded AAA counties received between $100,000 and $500,000 in AAA money

• Low-funded AAA counties received some AAA money, but less than $100,000

• Counties with no AAA-fund did not receive any funds.

Treat the following data as a random sample of voters within each county type. The results are based on the election results in the various counties.

(a) Do the data suggest that the level of funding received by counties through the AAA is associated with the candidate? Use the  level of significance.

(b) Construct a conditional distribution of candidate by level of AAA funding and draw a bar graph.

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Disneyland, the fairytale experience

In recent years, several projects involving amusement parks have emerged worldwide, offering different entertainment experiences to tourists. Yet, this growing market is faced with changes in consumer behaviors. Innovative attractions are no longer sufficient to satisfy consumers’ expectations. That is why improving the customer experience is crucial to retaining actual customers and attracting new ones. Disney created its first amusement park in the 1960s. The company places the visitor at the center of its efforts. Thus, it is essential to understand the story behind Disneyland’s success as well as the challenges and how it adapts to new visitors’ needs by enhancing the customer experience through different strategies to satisfy its tier customers and improve their loyalty.

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In the Manufacturing database, the Value of Industrial Shipments has been recoded into four classifications (1–4) according to magnitude of value. Let this value be the independent variable with four levels of classifications. Compute a one-way ANOVA to determine whether there is any significant difference n classification of the Value of Industrial Shipments on the Number of Production Workers (dependent variable). Perform the same analysis using End-of-Year Inventories as the dependent v ariable. Now change the independent variable to Industry Group, of which there are 20, and perform first a one-way ANOVA using Number of Production Workers as the dependent variable and then a one-way ANOVA using End-of-Year Inventory as the dependent variable.

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