Question

The daily revenue from the sale of fried dough at a local street vendor in Boston is known to be normally distributed with a known standard deviation of $120. The revenue on each of the last 25 days is noted, and the average is computed as $550. A 95% confidence interval is constructed for the population mean revenue. If the data from the last 40 days had been used, then the resulting 95% confidence intervals would have been _____________________.

Answer 1

Answer:

If the data from the last 40 days had been used, then the resulting 95% confidence intervals would have been narrower.

Step-by-step explanation:

The (1 - α)% confidence interval for the population mean is:

$CI=\bar x\pm z_{\alpha/2}\times \frac{\sigma}{\sqrt{n}}$

The width of this interval is:

$\text{Width}=2\times z_{\alpha/2}\times \frac{\sigma}{\sqrt{n}}$

The width of the confidence interval is inversely proportional to the sample size n.

This indicates a negative relationship between the width and sample size.

That is, as the value of sample size is increased the width would be decreased and if the sample size is decreased the width would be increased.

It is provided that the 95% confidence interval is constructed for the population mean revenue is computed using the data from last 25 days.

If the sample is increased from n = 25 to n = 40, the width of the interval will be decreased.

So, on increasing the sample size the confidence intervals would become narrower.