5 The following situation applies to Questions 510 In the 20

5. The following situation applies to Questions 5-10: In the 2004 election in Utah, 66% of all Utah voters voted for Amendment 3, the marriage amendment. Suppose a Statistics major decided to predict the sampling distribution of p for samples of size 100 for this situation. What is the mean of the sampling distribution of p? A. The mean equals p , which is 66%. O B. The mean equals p, which is 66%. O C. The mean will equal p, but we don\'t know what the value of p is.p

Solution

5.

The mean of these proportions will still be p, the population proportion, 66%.

Thus,

OPTION B: The mean equals p, which is 66%. [ANSWER]

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6.

s = sqrt(p(1-p)/n)

= sqrt(0.66*(1-0.66)/100)

= 0.047370877 [ANSWER]

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7.

B. It would stay the same. [ANSWER, B]

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8)

As we see, the standard deviation is inversely proportional to the square root of n. Thus,

OPTION C: The standard deviation would decrease.

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9.

By central limit theorem, the larger the sample size, the more bell shaped it is, so

B. The shape would be closer to normal. [ANSWER, B]

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10.

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    0.6      
x2 = upper bound =    0.7      
u = mean =    0.66      
          
s = standard deviation =    0.047370877      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -1.266600996      
z2 = upper z score = (x2 - u) / s =    0.844400664      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.102648998      
P(z < z2) =    0.800777224      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.6975 [ANSWER, A]