Question

Company “Text No Drive” is compiling background information for their new device that senses when texting is going on by the driver and stops the text. The company is interested in using injury statistics for their campaign. They compile information on the cost to the driver (in terms on injury and insurance costs) and also preferences by the driver.

The cost to the driver is described as average cost per injury depending on the amount of texting that the driver admits to doing. It is as follows:

Average cost	0	$800	$1,500	$3,000
Scale : Frequency of texting while driving	never	seldom	several times a week	every day
Number of injuries	7	17	28	43

They have piloted a program with the software and it yielded the following preferences for it:

Likert Scale: Preference for this product	1-Did not like it at all	2-Liked a few aspects of it	3-Liked many aspects of it	4-Liked it very much
Number of responses	12	24	45	14

1. What type of data is this?
2. Calculate the probabilities for: 1) each of the average cost categories, and 2) the type of preference for the product.
3. What is the probability that an average injury cost will be at least $800?
4. What is the average injury cost? What is the variance for the injury cost?
5. What is the probability that a person will like many aspects of the product?
6. What is the probability that a person will like only few aspects of the product?

Answer 1

(a)

Based on source of data, the type of data is primary data as the company piloted a program to collect data (not secondary type data as not collected from other source or not used for different purpose than that of collection).

Based on nature of data, the type of data is quantitative data as the data directly represents the amount in real numbers. Moreover, values possessing discrete (integral) values only, these are discrete quantitative data.

(b)

Suppose, random number X denotes the amount of average cost in different situation. Also random variable Y denotes the rating obtained in Likert scale.

(1)

Probabilities for each of the average cost categories are as follows.

Average cost (X)	$0	$800	$1500	$3000	Total
Scale: Frequency of texting while driving	never	seldom	several times a week	everyday	-
Number of injuries	7	17	28	43	95
Probability P(X=x)	7/95=0.074	17/95=0.179	28/95=0.295	43/95=0.452	1

(2)

Probabilities of type of preference for the product are as follows.

Likert scale (Y): Preference for this product	1-Did not it at all	2-Liked a few aspects of it	3-Liked many aspects of it	4-Liked it very much	Total
Number of responses	12	24	45	14	95
Probability P(Y=y)	12/95=0.126	24/95=0.253	45/95=0.474	14/95=0.147	1

(c)

Probability that average injury cost is at least $800 is given by

(d)

Average injury cost is given by

  

Now to calculate variance of injury cost we proceed as follows.

So, average injury cost $1941.7 and variance for the injury cost is 1076111.

(e)

Probability that a person will like many aspects of the product = P(Y=3) = 45/95 = 0.474

(f)

Probability that a person will like only few aspects of the product = P(Y=2) = 24/95 = 0.253