Final answer:
To estimate the population mean number of units sold per month, use the sample mean from collected data as the point estimate. This number can be further refined by calculating a confidence interval when the population standard deviation and sample size are known.
Step-by-step explanation:
To develop a point estimate of the population mean number of units sold per month, you would use the sample mean (×) as the best estimate. This involves collecting data on the number of units sold per month from a sample, calculating the mean of this sample, and then using this mean as the point estimate for the entire population. The formula for a point estimate is simply the sample mean, which is the sum of all sample values divided by the number of observations in the sample.
For example, if an entertainment company surveyed 100 customers and found that the sample mean of songs downloaded per month is x = 2, then the point estimate of the population mean would be 2 songs. To refine this estimate, the company can use the sample standard deviation and the size of the sample to calculate a confidence interval, stating the degree of certainty that the true population mean lies within this interval.
If the population standard deviation is known (in this case, σ = 1), and the sample size is n=100, according to the central limit theorem, the standard error (σ√n) would be 0.1. With this information, a 95% confidence interval can be calculated to be from x - 0.2 to x + 0.2, meaning we can be 95% confident that the true population mean lies within 1.8 to 2.2 songs downloaded per month.