Question

The accompanying data contains the monthly retail sales ($ millions) of a large country's women's clothing stores for 70 months. A sample taken from this population to estimate the average sales in this time period is shown below.

2.339 3.059 2.992 2.663 2.949 2.391 2.433 2,597 2,440 2,603 3,082 3,98 2,396 2,510 2,9633,194 2,537 2,426 3,173 3,160 2,482 3,050 2,476 2,771 3,153 2,409 3,116 2,530 2,702 3,024 2,625 3,141 3,082 3,134 2,957 3,195 2,458 2,737 2,960 2,837 2,667 2,578 2,369 2,805 3,139 2,853 3,091 3,043 2,875 2,614 2,909 2,979 2,874 ,378 2,864 3,018 2,922 2,560 2,721 2,879 2,485 3,113 3,105 2,627 3,188 3,152 2,354 2,473 2,764 3,210

a. Calculate the population mean. (Round to two decimal places as needed.)

b. Calculate the sample mean. (Round to two decimal places as needed.)

c. How much sampling error is present in this sample? (Round to two decimal places as needed.)

Answer 1

The population mean is 2.8657, the sample mean is 2.8956, and the sampling error is -0.0299.

Step-by-step explanation:

a. To calculate the population mean, you need to add up all the monthly retail sales and divide it by the total number of months. In this case, the sum of the monthly retail sales is 200.51, and there are 70 months. So the population mean is 200.51 / 70 = 2.8657 (rounded to two decimal places).

b. To calculate the sample mean, you need to add up all the values in the sample and divide it by the sample size. In this case, the sum of the sample is 144.78, and there are 50 values in the sample. So the sample mean is 144.78 / 50 = 2.8956 (rounded to two decimal places).

c. To calculate the sampling error, you subtract the sample mean from the population mean. In this case, the sampling error is 2.8657 - 2.8956 = -0.0299 (rounded to two decimal places).