Question

An analyst at Umbrella Corporation studied the relationship between the sales (in millions of dollars) of a product (Y) and population (in millions of people) in the company's 50 marketing districts. After fitting the simple linear regression model Y βo+β1(population) +E the analyst found that a 95% confidence interval for the slope, β1 , was [0453, 1 061
What is the "real-world" interpretation of this interval?
1. The company can claim that 95% of sales in a marketing district with 1 million people will be between S453 000 and $1,060,000
2. The company can be 95% confident that the true mean sales in the marketing district are between $453,000 and $1,060,000. ?
3. The company can be 95% confident that the mean sales for each additional 1 m llion persons in the unincrease marketing district is between $453,000 and $1,060,000.
4. The company can be 95% confident that ota se es for 1 million persons in the marketing district will be between $453,000 and $1,060,000
5. The company can be 95% confident that the rue mean sales when the population is 0 is between S4 53,000 and $1,060,000

Answer 1

Answer:

OPTION A: The company can be 95% confident, based on the method used to calculate the interval, that the true increase in mean sales for each additional 1 million persons in the marketing district is between $453,000 and $1,060,000.

Step-by-step explanation:

Note that the slope here is the increase in sales (in millions of dollars) per every 1 million increase in population. Hence, as this is a confidence interval for the slope, then

OPTION A: The company can be 95% confident, based on the method used to calculate the interval, that the true increase in mean sales for each additional 1 million persons in the marketing district is between $453,000 and $1,060,000.