Texmac, Inc., has an idea for a new type of weaving machine that could replace the machines now used by many textile manufacturers. Texmac has done a telephone survey to estimate how many of the old-style machines are now in use. Respondents using the present machines were also asked if they would buy the improved machine at a price of $10,000.
Texmac researchers identified a population of about 5,000 textile factories as potential customers. A sample of these were surveyed, and Texmac received 500 responses. Researchers think the total potential market is about 10 times larger than the sample of respondents. Two hundred twenty of the respondents indicated that their firms used old machines like the one the new machine was intended to replace. Forty percent of those firms said that they would be interested in buying the new Texmac machine.
Texmac thinks the sample respondents are representative of the total population, but the marketing manager realizes that estimates based on a sample may not be exact when applied to the whole population. He wants to see how sampling error would affect profit estimates. Data for this problem appear in the spreadsheet. Quantity estimates for the whole market are computed from the sample estimates. These quantity estimates are used in computing likely sales, costs, and profit contribution.
a. An article in a trade magazine reports that there are about 5,200 textile factories that use the old-style machine. If the total market is really 5,200 customers—not 5,000 as Texmac originally thought—how does that affect the total quantity estimate and profit contribution?
b. Some of the people who responded to the survey didn’t know much about different types of machines. If the actual number of old machines in the market is really 200 per 500 firms—not 220 as estimated from survey responses—how much would this affect the expected profit contribution (for 5,200 factories)?
c. The marketing manager knows that the percentage of textile factories that would actually buy the new machine might be different from the 40 percent who said they would in the survey. He estimates that the proportion that will replace the old machine might be as low as 36 and as high as 44 percent—depending on business conditions. Use the analysis feature to prepare a table that shows how expected quantity and profit contribution change when the sample percent varies between a minimum of 36 and a maximum of 44 percent. What does this analysis suggest about the use of estimates from marketing research samples? (Use 5,200 for the number of potential customers and use 220 as the estimate of the number of old machines in the sample.)