Question

A random sample of 81 credit sales in a department store showed an average sale of $68. 0. From past data, it is known that the standard deviation of the population is $27. 0. A. Determine the standard error of the mean. B. What is the 95% confidence interval of the population mean?

Answer 1

Explanation:

A. To determine the standard error of the mean, we can use the formula:

Standard Error = population_standard_deviation / sqrt(sample_size)

In this case, the population standard deviation is given as $27.0, and the sample size is 81.

Standard Error = 27.0 / sqrt(81) = 27.0 / 9 = 3.0

Therefore, the standard error of the mean is $3.0.

B. To calculate the 95% confidence interval of the population mean, we can use the formula:

Confidence Interval = sample_mean ± (critical_value * standard_error)

The critical value is based on the desired confidence level and can be obtained from a t-distribution table. For a 95% confidence level with a sample size of 81, the critical value is approximately 1.984.

Sample Mean = $68.0 (given)

Standard Error = $3.0 (calculated in part A)

Confidence Interval = 68.0 ± (1.984 * 3.0)

Confidence Interval = 68.0 ± 5.952

Therefore, the 95% confidence interval of the population mean is ($62.048, $73.952). This means that we are 95% confident that the true population mean falls within this range.