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: 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. How does compare to x/n? 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 = .80 for the entire sample of 25 cars?

Answer : Step 1 of 3 : Given, 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 S S S F F S S a) The claim is to find the value of the sample proportion of successes x/n Where, S be the success We have s = 7 The proportion of success = 7/10 = 0.7 Step 2 of 3 : b) replace each S with a 1 and each F with a 0 and the claim is to calculate the mean and compare to x/n. Then the data be : 1 1 0 1 1 1 0 0 1 1 x = x n Where, x = 7 and n = 10 07 x = 10 = 0.70 Which is equal to the sample proportion of the success.