Chapter 25, Problem 11E

(a)

To determine

To explain which of the summaries would help you decide whether the online company offers cheaper insurance and why.

Answer to Problem 11E

The histogram.

Explanation of Solution

From the previous question we get the summary statistics for ten drivers’ car insurance premiums quoted by a local agent and an online company. The box plot for the same is given and the scatterplot of the price difference “PriceDiff” is given in the question. Thus, from these two the histogram would help you decide whether the online company offers cheaper insurance because the variables are not independent (subjects are the same cars) and thus we are interested in the distribution of the differences for each car.

(b)

To determine

To discuss why the standard deviation of PriceDiff is quite a bit smaller than the standard deviation of price quoted by either the local or online companies.

Explanation of Solution

From the previous question we get the summary statistics for ten drivers’ car insurance premiums quoted by a local agent and an online company. The box plot for the same is given and the scatterplot of the price difference “PriceDiff” is given in the question. Thus, from these two the histogram would help you decide whether the online company offers cheaper insurance. Thus, the standard deviation of PriceDiff is quite a bit smaller than the standard deviation of price quoted by either the local or online companies because the differences for the same cars will have a smaller variability than differences for independent cars, because the independent cars will most likely have different properties. This then means that the standard deviation for the differences will be smaller than the standard deviation for the assumed to be "independent" variables.

(c)

To determine

To discuss the assumptions and conditions for inference with these data.

Answer to Problem 11E

All the conditions are met.

Explanation of Solution

From the previous question we get the summary statistics for ten drivers’ car insurance premiums quoted by a local agent and an online company. The box plot for the same is given and the scatterplot of the price difference “PriceDiff” is given in the question. Thus, from these two the histogram would help you decide whether the online company offers cheaper insurance. Thus, the assumptions and conditions for inference with these data is as follows:

Random condition: It is satisfied because the profiles were randomly selected.

Independent condition: It is satisfied because the ten people selected profiles were less than $10\%$ of the population.

Normal condition: It is satisfied because the histogram is symmetric and uni-modal as shown in the question.

Thus, all the conditions are met.