How to build a 90% Confidence Interval for Profit (When price competitor Pc=5, Wage W=$11)

To build a 90% confidence interval for profit, you will need data on the profits of your business. Specifically, you will need a sample of profit observations.

Once you have the profit data, you can use the following steps to construct a 90% confidence interval:

1. Calculate the sample mean (x̄) and standard deviation (s) of the profit data.

- The sample mean (x̄) is calculated by summing up all the profit values and dividing it by the total number of observations.
- The standard deviation (s) is a measure of the dispersion or variability in the profit data. It quantifies how spread out the profit values are from the mean.

2. Determine the sample size (n) of the profit data.

3. Calculate the standard error (SE), which is a measure of the uncertainty in the sample mean. It is calculated using the formula: SE = s / √n.

4. Determine the critical value (z*) from the standard normal distribution table. For a 90% confidence interval, the z* value will be the value that leaves 5% in the tails of the distribution. In this case, the z* value will be approximately 1.645.

5. Calculate the margin of error (ME) using the formula: ME = z* * SE.

6. Finally, construct the confidence interval by subtracting and adding the margin of error to the sample mean:

- Lower limit = x̄ - ME
- Upper limit = x̄ + ME

Using these steps, you can create a 90% confidence interval for profit. However, note that this analysis assumes that the profit data is a random sample from the population of interest and satisfies the assumptions of the method being used. Additionally, keep in mind that the prices of competitors and wages may be factors affecting profit but may not be directly utilized in calculating the confidence interval.