1. 3M has developed a composite measure, a 3M™ Value Index Score, which provides a standard metric to assess accountable value in health care. This index score is a composite measure based on six critical primary care domains derived from 16 measures of key processes and outcomes that effect value in health care. According to 3M, this Value Index Score can increase the understanding of provider and system performance thereby accelerating and prioritizing the areas where improvement is needed. This measure can be used by both providers and payers to help improve patient outcomes and to control costs. Suppose you were asked to develop a sampling plan for a study to determine the value of the index, usage rates of the index, and general attitudes toward the index, what sampling plan would you use? What is the target population (or are there multiple target populations)? What might you use for the frame(s)? Which of the four types of random sampling discussed in the chapter would you use and why? If you were to use stratified random sampling, what would be your strata?
2. In 2009, the Global Strategy Group conducted an online survey commissioned by Scotch® Tape of adults nationwide in the United States about their personal gift-wrapping behaviors and trends. One finding was that the average number of presents wrapped by adults in a typical December holiday season is 15.3. In addition, the study found that women wrap more presents than men with women averaging 20.3 and men averaging 9.9. Suppose that these figures obtained from a sample are actually true for the entire population and that the standard deviation for all adults, for women, and for men is 2.5. If a random sample of 35 U.S. adults is taken, what is the probability that the sample mean number of presents wrapped in a typical December holiday season is more than 16? If a random sample of 60 U.S. men is taken, what is the probability that the sample mean number of presents wrapped by a man in a typical December holiday season is less than 10? If a random sample of 43 U.S. women is taken, what is the probability that the sample mean number of presents wrapped by a woman in a typical December holiday season is between 20.0 and 20.8?
3. In 2015, 3M commissioned a survey conducted by Wakefield Research regarding color quality in electronic devices (phones, tablets, notebook PC’s and LCD TVs). Among the results of the survey are that 62% of device owners wish there was better color quality on their display devices. Twenty-nine percent want more realistic colors, eighteen percent want bolder colors, and fourteen percent want richer dark colors. Assume these figures are true for the general population of device owners. If a random sample of 450 device owners is taken, what is the probability that more than 65% wish there was better color quality on their display devices? If a random sample of 270 device owners is taken, what is the probability that 25% or fewer want more realistic colors? If a random sample of 950 device owners is taken, what is the probability that between 152 and 200 want bolder colors?
The 3M company is a global innovation company with over 100,000 patents, $31 billion in sales, and 90,000 employees. 3M has 27 business units organized under five business groups: consumer, electronics & energy, health care, industrial, and safety & graphics. It has 46 technology platforms including adhesives, abrasives, electronics & software, light management, microreplication, nanotechnology, nonwoven materials, and surface modification. Related to this, 3M has 8,500 researchers worldwide and its products are sold in nearly 200 countries. Included in 3M’s more widely-known products are Scotch® Tape, Post-it® Notes, and Ace™ bandages.
3M was born as a small-scale mining company in 1902 when the five founders invested in harvesting a mineral known as corundum from a mine in Minnesota on the shores of Lake Superior. The mine ultimately did not produce much corundum but the company used a spirit of innovation, collaboration, and technology to discover other materials and products that could be of use to consumers and companies. In 1910, the company, then known as Minnesota Mining and Manufacturing (3M), moved its headquarters to St. Paul where it is today. In the early 1920s, 3M created the world’s first waterproof sandpaper which helped open up opportunities for the company in the automotive industry. In 1925, a young lab assistant invented masking tape thereby helping to diversify the company’s offering. Over the next few decades, many of the “Scotch™” products were developed and marketed including Scotch® Tape, Scotchlite™, and Scotchgard™. In the 1960’s, 3M introduced dry silver microfilm, photographic products, carbonless papers, overhead projection systems, and numerous health care and dental products. In 1980, 3M introduced Post-it® Notes creating a new category in the marketplace. By the year 2000, there were new products such as Post-it® Super Sticky Notes, Scotch® Transparent Duct Tape, optical films for LCD televisions and a family of new Scotch-Brite™ Cleaning Products. In 2009, 3M introduced a new line of stethoscopes in health care and introduced new produces in the grinding industry. In later years, 3M developed 3M® Solar Mirror Film 1100 for concentrated solar power.
Today, one-third of 3M’s sales come from products invented within the past five years during which time over $8 billion has been invested in R&D and related expenditures. According to company information sources, the global 3M team is committed to creating the technology and products that advance every company, enhance every home and improve every life. 3M has been listed on the Dow Jones Sustainability Index for 15 consecutive years.
