A random sample of 500 reports an average yearly income of $42,000 with a standard deviation of $1000. An estimate of the parameter at the 95% level is about $175 wide. In this research situation________.
A) we can be 95% confident that the population mean is 42,000 ± 175.
B) the sample size is much too small to justify the use of estimation procedures.
C) the alpha level is 1000.
D) the sample mean is $175.

Question

Quizplus · Accepted Answer

The estimate of the parameter at the 95% level being approximately $175 wide means that the margin of error is $175. Thus, we can create a 95% confidence interval using the sample mean and the margin of error to state that we are 95% confident that the population mean falls within the interval. Therefore, option A is the best choice. Option B is incorrect because a sample size of 500 is considered large enough to use estimation procedures. Option C is incorrect because the given standard deviation value of $1000 is not the alpha level. Option D is incorrect because the sample mean is $42,000, not $175.

A Random Sample of 500 Reports an Average Yearly Income