Question

A survey was conducted of 250 pediatricians on the average age of their patients. A sample mean of 8.3 years was determined, with a standard deviation of 1.8 years. Assuming a 90% confidence level, which of the following statements holds true?
A. As the sample size is too small, the margin of error cannot be trusted.


B. As the sample size is too small, the margin of error is ±1.029.


C. As the sample size is appropriately large, the margin of error is ±0.187.


D. As the sample size is appropriately large, the margin of error is ±0.014.

Answer 1

A sample size of 250 is a Large Enough sample.

If no information is given about the population and the sample size is above 30 or 40, we can assume that the population is normally distributed. In this case the sample size is 250. So this is a large enough sample size.

Since population standard deviation is not known, we will use t distribution to find the margin of error.

M.E=±$t_{crit}* \frac{s}{ \sqrt{n} }$

The critical t value for 90% confidence level and 249 degrees of freedom comes out to be 1.65

So,


M.E=±$1.65* \frac{1.8}{250}=0.187$

Thus option C gives the correct answer

Answer 2

Answer:

1.65 × (1.8÷ √250) = 0.1878 so C