A sample of n = 10 automobiles was selected, and each was subjected to a 5-mph c

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   F   F   F   F   F   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.

(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 = 0.4 for the entire sample of 25 cars?

Explanation / Answer

there are 10 automobiles.

Denoting a car with no visible damage by S (for success) and a car with such damage by F, results were as follows:

S   F   F   F   F   F   S   F   S   S

so there are 4 S and 6 F

a) so the sample proportion of success is =total number of S/n=4/10=0.4

b) replacing S with 1 and F with 0

we get the coded data as

1 0 0 0 0 0 1 0 1 1

then x=total number of success=number of 1's in the data=4 [answer]

c)

now 15 more cars are included

so now n=25

we want x/n to be 0.4

or, x/n=0.4 or, x=25*0.4=10

there are already 4 S.

so out of 15 newly included cars we should have 10-4=6 cars to be S [answer]

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