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 $175 wide.In this research situation,
A)we can be 95% confident that the population mean is 42,000$\pm$ 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

Using the sample mean of $42,000, the standard deviation of $1000, and a 95% confidence level, we can construct a confidence interval for the population mean. The margin of error is estimated to be about $175 (given in the question). Therefore, the 95% confidence interval would be:

$42,000 ± $175

or

($41,825, $42,175)

This means that we can be 95% confident that the true population mean falls within this interval.

A Random Sample of 500 Reports an Average Yearly Income ±\pm±

A Random Sample of 500 Reports an Average Yearly Income $\pm$