Chapter 9 Case Study
Statistics – Case Chapter 9
1. It is not proper to multiply the average order size by the number of addresses (1.3 million people = population) in the target mailing because the sample is representative of the 600,000 people in the database, not the 1.3 million target population, thus you cannot use the average of the sample as an estimate for the population. Also, multiplying by 1.3 million would suggest that the entire 1.3 million people would be purchasing.
2. It is better to multiply the endpoints of the confidence interval by the population because now there will be a range of values, but it still will not be accurate because the confidence interval is still using the mean from the sample, which isn’t representative of the population, thus it cannot be used as an estimate for the population. In this situation, there will be far less than 1.3 million people purchasing from the catalog thus using the lower limit of the confidence interval will still be far higher than the actual amount.
3. It is also better to use the size of the frame (600,000 people from the database) since our sample is representative of the 600,000 people in the database, thus we can use the mean of the sample as an estimator for the 600,000 people in the database. However, only 13 people of the 600 sample responded with a yes and a dollar amount, thus multiplying the mean of the 13 people who responded with an intent to purchase by the 600.000 people in the database will also give you a much higher amount for the lower bound of the confidence interval than the actual amount.
4. This situation is very troubling for many reasons. The response rate (9%) for the survey is an early indication of trouble, there were only 55 responses from the 600 people sampled, and only 13 of those indicated intent to purchase. Also, the sample was selected randomly from the 600,000 person database, but the 600,000 person database isn’t random, since they were selected based on being well-off. The
1. It is not proper to multiply the average order size by the number of addresses (1.3 million people = population) in the target mailing because the sample is representative of the 600,000 people in the database, not the 1.3 million target population, thus you cannot use the average of the sample as an estimate for the population. Also, multiplying by 1.3 million would suggest that the entire 1.3 million people would be purchasing.
2. It is better to multiply the endpoints of the confidence interval by the population because now there will be a range of values, but it still will not be accurate because the confidence interval is still using the mean from the sample, which isn’t representative of the population, thus it cannot be used as an estimate for the population. In this situation, there will be far less than 1.3 million people purchasing from the catalog thus using the lower limit of the confidence interval will still be far higher than the actual amount.
3. It is also better to use the size of the frame (600,000 people from the database) since our sample is representative of the 600,000 people in the database, thus we can use the mean of the sample as an estimator for the 600,000 people in the database. However, only 13 people of the 600 sample responded with a yes and a dollar amount, thus multiplying the mean of the 13 people who responded with an intent to purchase by the 600.000 people in the database will also give you a much higher amount for the lower bound of the confidence interval than the actual amount.
4. This situation is very troubling for many reasons. The response rate (9%) for the survey is an early indication of trouble, there were only 55 responses from the 600 people sampled, and only 13 of those indicated intent to purchase. Also, the sample was selected randomly from the 600,000 person database, but the 600,000 person database isn’t random, since they were selected based on being well-off. The