Confidence Intervals in Business

Confidence Intervals in Business

Confidence intervals are a useful business tool for estimating the range of values around a sample statistic, such as a mean or proportion, within a given level of confidence. Businesses, for example, frequently use confidence intervals to forecast sales projections, marketing results, and customer satisfaction rates (Black, 2020). Setting pricing strategies is one specific business decision that could benefit from confidence intervals. Suppose a company is considering raising the price of a product or service. The company can estimate the potential impact of the price increase on sales revenue using a confidence interval (Cheah et al., 2020). The business can determine a range of possible outcomes with a certain level of confidence by calculating the confidence interval, which can help them make a more informed decision.

For example, consider a software company considering raising the price of its premium software package from $150 to $200. The company can use a confidence interval to estimate the impact of the price increase on sales revenue. Using historical data on the number of units sold at each price point, the company can calculate the confidence interval around the mean revenue from the previous year. By doing so, it can estimate the range of possible outcomes with a high level of confidence, such as a 95% confidence interval.

Confidence Interval Problem

A recent survey of 100 college students found that the mean number of hours they spent studying per week was 12 hours, with a standard deviation of 2 hours. Calculate a 99% confidence interval for the true mean number of hours college students spend studying per week.

Use the formula for confidence interval:

CI = X̄ ± Z(α/2) * (s/√n)

Where:

X̄ = sample mean (12 hours)

s = sample standard deviation (2 hours)

n = sample size (100)

α = level of significance (1 – confidence level) = 0.01/2 = 0.005

Z(α/2) = the z-score associated with the α/2 level of significance (from the z-table, for a 99% confidence level, Z(0.005) = 2.576)

References

Black, K. (2020). Business Statistics: For Contemporary Decision Making. (10th ed.). Wiley & Sons.

Cheah, J.-H., Thurasamy, R., Memon, M. A., Chuah, F., & Ting, H. (2020). Multigroup analysis using SmartPLS: Step-by-Step guidelines for business research. Asian Journal of Business Research, 10(3). https://doi.org/10.147

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Consider when businesses might use confidence intervals to estimate values, such as in sales projections, marketing results, and so forth. Describe a business decision that could be helped with confidence intervals. Be specific! Then create a problem with numbers from which another student could calculate a confidence interval and make a decision

References:
1. Black, K. (2019). Business Statistics: For Contemporary Decision Making. In Google Books (10th ed.). John Wiley & Sons.