A sample survey of 62 discount brokers showed that the mean price charged for a trade of 100 shares at $50 per share was $31.22. The survey is conducted annually. With the historical data available, assume a known population standard deviation of $19. (a) Using the sample data, what is the margin of error in dollars associated with a 95% confidence interval? (Round your answer to the nearest cent.) $ (b) Develop a 95% confidence interval for the mean price in dollars charged by discount brokers for a trade of 100 shares at $50 per share. (Round your answers to the nearest cent.) $ to $

a) The margin of error associated with a 95% confidence interval is of $4.73.

b) $26.49 to $35.95

Step-by-step explanation:

Question a:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find the margin of error M as such

In which is the standard deviation of the population and n is the size of the sample.

The margin of error associated with a 95% confidence interval is of $4.73.

Question b:

The lower end of the interval is the sample mean subtracted by M. So it is 31.22 - 4.73 = $26.49

The upper end of the interval is the sample mean added to M. So it is 31.22 + 4.73 = $35.95

So $26.49 to $35.95

i believe the correct answer is b.