the standard error of most sample estimators approaches zero as sample size increases so almost

1. First, we need to set up our null and alternative hypotheses. The null hypothesis (H0) is tha

Question

The standard error of most sample estimators approaches zero as the sample size increases, so almost any difference between the sample statistic and the hypothesized parameter value, no matter how tiny, will be significant if the sample size is large enough. Researchers who deal with large samples must expect "significant" effects, even when an effect is too slight to have any practical importance. Is an improvement of 0.2 mpg in fuel economy important to Toyota buyers? Is a 0.5 percent loss of market share important to Hertz? Is a laptop battery life increase of 15 minutes important to Dell customers? Such questions depend not so much on statistics as on a cost/benefit calculation. Since resources are always scarce, a dollar spent on a quality improvement always has an opportunity cost (the foregone alternative). If we spend money to make a certain product improvement, then some other project may have to be shelved. Since we can't do everything, we must ask whether a proposed product improvement is the best use of our scarce resources. These are questions that must be answered by experts in medicine, marketing, product safety, or engineering, rather than by statisticians. As an example, consider the following question. Suppose we want to compare the IQ test scores of high school students from two different states. In Nevada, we sample 12,000 students and find a mean of 100.15 with a standard deviation of 15. In New Jersey, we sample 188,000 students and find a mean of 99.85 with a standard deviation of 14.75. a) Test if there is a difference in the average IQ of students between the two states. Show your implementation in Minitab. b) Discuss practical versus statistical significance for this example and provide relevant citations.

The standard error of most sample estimators approaches zero as the sample size increases, so almost any difference between the sample statistic and the hypothesized parameter value, no matter how tiny, will be significant if the sample size is large enough. Researchers who deal with large samples must expect "significant" effects, even when an effect is too slight to have any practical importance. Is an improvement of 0.2 mpg in fuel economy important to Toyota buyers? Is a 0.5 percent loss of market share important to Hertz? Is a laptop battery life increase of 15 minutes important to Dell customers? Such questions depend not so much on statistics as on a cost/benefit calculation. Since resources are always scarce, a dollar spent on a quality improvement always has an opportunity cost (the foregone alternative). If we spend money to make a certain product improvement, then some other project may have to be shelved. Since we can't do everything, we must ask whether a proposed product improvement is the best use of our scarce resources. These are questions that must be answered by experts in medicine, marketing, product safety, or engineering, rather than by statisticians. As an example, consider the following question. Suppose we want to compare the IQ test scores of high school students from two different states. In Nevada, we sample 12,000 students and find a mean of 100.15 with a standard deviation of 15. In New Jersey, we sample 188,000 students and find a mean of 99.85 with a standard deviation of 14.75.

a) Test if there is a difference in the average IQ of students between the two states. Show your implementation in Minitab.

b) Discuss practical versus statistical significance for this example and provide relevant citations.

Added by Jason B.