Suppose the mean of dogs a pet shop grooms each day is known to be 14.2 dogs. If a sample of n=12 days is chosen and a total of 178 dogs are groomed during those 12 days, then the sampling error is?
To calculate the sampling error, we first need to find the average number of dogs groomed per day in the sample.
The average number of dogs groomed per day is the total number of dogs groomed during the sample period divided by the number of days in the sample:
Average = Total number of dogs groomed / Number of days
In this case, the total number of dogs groomed during the 12-day sample period is 178 dogs. The number of days in the sample is 12. Let's plug these values into the formula:
Average = 178 dogs / 12 days
Average ≈ 14.83 dogs per day
Now we can calculate the sampling error by taking the absolute difference between the sample mean and the known population mean:
Sampling Error = |Sample Mean - Population Mean|
In this case, the population mean is given as 14.2 dogs per day. The sample mean we calculated is approximately 14.83 dogs per day. Plug these values into the formula:
Sampling Error = |14.83 - 14.2|
Sampling Error ≈ 0.63
Therefore, the sampling error is approximately 0.63 dogs per day.