7. A firm has appointed a large number of dealers all over the country to sell its bicycle; it is interested in knowing the average sales per dealer. A random sample of 25 dealers is selected for this purpose, the sample mean is birr 50,000 and sample standard deviation is 20,000. The population of sales is approximately normal. Construct an interval estimate with 99 % confidence level.

Question

7. A firm has appointed a large number of dealers all over the country to sell its bicycle; it is interested in knowing the average sales per dealer. A random sample of 25 dealers is selected for this purpose, the sample mean is birr 50,000 and sample standard deviation is 20,000. The population of sales is approximately normal. Construct an interval estimate with 99 % confidence level.

Answer 1

To construct an interval estimate with a 99% confidence level, we can use the formula for a confidence interval for the population mean.

The formula is:

Confidence Interval = sample mean ± (critical value * standard deviation / √n)

First, let's find the critical value for a 99% confidence level. Since the population is assumed to be approximately normal, we can use a Z-table to find the critical value. For a 99% confidence level, we need to find the Z-value that leaves 0.5% in each tail. This corresponds to an area of 0.005 in the upper tail. By looking up the Z-value in the table or using a calculator, we find that the critical value is 2.576.

Now, we can substitute the given values into the formula:

Confidence Interval = 50,000 ± (2.576 * 20,000 / √25)

Simplifying the formula:

Confidence Interval = 50,000 ± (2.576 * 20,000 / 5)

Confidence Interval = 50,000 ± (2.576 * 4,000)

Confidence Interval = 50,000 ± 10,304

Therefore, the interval estimate with 99% confidence level for the average sales per dealer is (39,696, 60,304). This means we are 99% confident that the true average sales per dealer falls within this range.