Package Design

The Kenton Food Company wished to test four package designs for a new breakfast cereal. Twenty stores were selected as the experimental units. Each store was randomly assigned one of the package designs, with each design assigned to five stores. The stores were chosen to be comparable in location and sales volume. Other relevant conditions that could affect sales, such as price, amount and location of shelf space, and special promotional efforts, were kept the same for all the stores in the experiment. Sales, in number of cases, were recorded for the study period, and the results recorded in the table below.

1. Prepare side-by-side box-and-whisker plots to compare sales for the four package designs.
   1. Does there appear (just by looking at the plot) to be any difference in variability in sales among the four designs? How can you tell?
   2. Do average sales appear do differ according to package design? How can you tell?
2. Assuming that the variability in sales does not depend on the package design, test the null hypothesis that the mean number of cases sold does not vary according to package design. State your conclusion and indicate how you reached it.
   
   
3. Use the Tukey procedure for multiple comparisons with familywise significance level 0.05 to determine which, if any, designs are superior to the others, in terns of mean sales. Summarize your findings.
   
   
4. Suppose that the characteristics of the four package designs are as follows:

Using individual significance level of 0.05 for each.

1. Test the hypothesis that on the average, sales are higher using 5 colors than when using 3 colors. State your conclusion.
   
2. Test the null hypothesis that on the average, cartoons do not make any difference.
   
3. Test the hypothesis that if 3 colors are used, sales are higher when cartoons are used.
   
4. Test the hypothesis that if cartoons are used, sales are higher when 5 colors are used than when 3 colors are used.
   
5. Test the hypothesis that Design 4 is superior to the other three.

M & M Candies

The Masterfoods Company says that yellow candies make up 20% of its milk chocolate M&Ms, red another 20%, orange, green and blue 10% each, and the rest are brown.

I bought a bag of plain M&Ms and got 29 yellow ones, 23 red, 12 orange, 14 blue, 8 green, and 20 brown. Is this sample consistent with the company’s stated proportions?

Support your answer statistically.

Race and Education

Data from the U.S. Census Bureau show levels of education attained by age 30 for a sample of U.S. residents. Do these data highlight significant differences in educational levels attained by these groups? Support your answer statistically.

Sea Fans

Coral reef communities are home to one quarter of all marine plants and animals worldwide. These reefs support large fisheries by providing breeding grounds and safe havens for young fish of many species. Coral reefs are sea walls that protect shore lines against tides, storm surges, and hurricanes, and are sand "factories" that produce the limestone and sand of which beaches are made. Beyond the beach, these reefs are major tourist attractions for snorkelers and divers, driving a tourist industry worth billions of dollars.

But marine scientists say that 10% of the world’s reef systems have been destroyed in recent times. At current rates of loss, 70% of the reefs could be gone in 40 years. Pollution, global warming, outright destruction of reefs, and increasing acidification of the oceans are all likely factors in this loss.

Dr. Drew Harvell’s lab studies corals and the diseases that affect them. They sampled sea fans at 19 randomly selected reefs along the Yucatan peninsula and diagnosed whether the animals were affected by the disease aspergillosis . In specimens collected at a depth of 40 feet at the Las Redes Reef in Akumal, Mexico, these scientists found that 54 of the 104 sea fans sampled were infected with that disease.

Of course, we care about much more than these particular 104 sea fans. What can this study tell us about the prevalence of the disease among sea fans in coral reef communities in the Caribbean?

Home Field Advantage

Anyone who plays or watches sports has heard of the home field advantage". Teams tend to win more often when they play at home. Or do they?

If there were no home field advantage, then home teams would win about half of all games played. In the 2006 Major League Baseball season, there were 2419 regular-season games. (One rained-out game was never made up.) It turns out that the home team won 1327 of the 2419 games. Could this be just natural sampling variability, or is it evidence to suggest that there really is a home field advantage, at least in professional baseball?

Price: $29.54

Solution: The downloadable solution consists of 14 pages, 1554 words and 11 charts.
Deliverable: Word Document