Factories use one-sample t-tests to determine if the quality of their product is
ID: 3183154 • Letter: F
Question
Factories use one-sample t-tests to determine if the quality of their product is consistent. For example, Frito Lay randomly pulls a sample of 30 bags of chips from the line, calculates the average weight of the bags along with the standard deviation, and compares that mean to the weight stated on the bag (considered the population mean). In this example, Frito Lay would not want significant differences between the mean weight of the sample and the population mean. Identify at least three other real world situations in which we would want to compare a sample mean to a set or population mean.For each situation you listed explain how you would conduct the test to determine if the sample mean is significantly different from the population mean
Explanation / Answer
1. A generic brand of the anti-histamine Diphenhydramine markets a capsule with a 50 milligram dose. The manufacturer is worried that the machine that fills the capsules has come out of calibration and is no longer creating capsules with the appropriate dosage. The company randomly pulls a sample of 30 capsules from the line, calculates the average weight of the capsules along with the standard deviation, and compares that mean to 50 mg. (considered the population mean).
2. The mean height of adults ages 20 and older is about 66.5 inches (69.3 inches for males, 63.8 inches for females). Let's test if the mean height of our sample data is significantly different than 66.5 inches using a one-sample t test. Take a random sample of 100 adults, and calculate the sample mean and standard deviation of height and compare it with the population height (66.5 inches).
3. The NCHS (National Center for Health Statistics) report indicated that in 2002 Americans paid an average of $3,302 per year on health care and prescription drugs. An investigator hypothesizes that in 2005 expenditures have decreased primarily due to the availability of generic drugs. To test the hypothesis, a sample of 100 Americans are selected and their expenditures on health care and prescription drugs in 2005 are measured. The sample mean is compared with the population mean to determine the t-statistic and if there is any significant difference between the sample and population mean ($3,302).
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