Question

1a. 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:

F F S S S F F S F F

(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 = 0.76 for the entire sample of 25 cars?

___ cars

2b. A study of the relationship between age and various visual functions (such as acuity and depth perception) reported the following observations on the area of scleral lamina (mm2) from human optic nerve heads:

2.74 2.67 2.73 3.79 2.33 2.65 3.88 4.16 3.87   

4.40 3.45 4.61 2.50 3.55 2.75 3.51 3.08   

(a) Calculate Σxi and Σxi2. (Round Σxi2 to two decimal places.)

Σxi = ____ mm2

Σxi2 =_____ mm4

(b) Use the values calculated in part (a) to compute the sample variance s2 and then the sample standard deviation s. (Round your answers to three decimal places.)

s2 = _____mm4

s =______ mm2

Answer 1