Question

A sample of n = 10 automobiles was selected, and each was subjected to a 5-mph crash test. Denoting a car with no visible damage by S (for success) and a car with such damage by F, results were as follows: S S F F F S S F S S (a) What is the value of the sample proportion of successes x/n? (b) Replace each S with a 1 and each F with a 0. Then calculate x for this numerically coded sample. x = How does x compare with x/n? The proportion in part (a) is exactly equal to the mean in part (b). The proportion in part (a) is greater than the mean in part (b). The proportion in part (a) is less than the mean in part (b). (c) Suppose it is decided to include 15 more cars in the experiment. How many of these would have to be S's to give x/n = 0.52 for the entire sample of 25 cars? cars

Answer 1

(a) x/n=0.6

(b) is exactly equal to the mean

(c) 7 cars

Explanation:

(a) We have a test with n=10 cars, were 6 of them succeded (x=6) and 4 of them failed.

The proportion of successes x/n is 6/10=0.6.

(b) If we replaced S by 1 and F by 0, we have the same result

`sum/n=(6*1+4*0)/10=6/10=0.6`

(c) If they include 15 more cars to a total of n=25 cars, to have a proportion of successes of 0.52, it is expected to have 7 successes out of the 15 new cars:

`(x/n)=0.52=(6+x_2)/(10+15)\\\\x_2=(0.52*25-6)/15=7`