Government data show that 9 % of the American population are at least 75 years o

Question

Government data show that 9% of the American population are at least 75 years of age. To test a random-digit dialing device, you use the device to call randomly chosen residential telephones in your county. Of the 280 members of the households contacted, 5% are 75 years or older.

(a) Is each of the boldface numbers a parameter or a statistic?

a.9%: statistic, 5%: statistic

b.9%: parameter, 5%: parameter    

c.9%: parameter, 5%: statistic

d.9%: statistic, 5%: parameter

(c) What is the probability that a random sample of 280 respondents would contain less than 5% of individuals at least 75 years of age? (Use 3 decimal places)

Explanation / Answer

Note that parameters are for populations, and statistics are for samples.

a)

OPTION C: c.9%: parameter, 5%: statistic [ANSWER]

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b)

Here,  
n =    280
p =    0.09

Hence,

u = mean = p =    0.09   [ANSWER]  
          
s = standard deviation = sqrt(p(1-p)/n) =    0.017102631   [ANSWER]

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c)  
          
We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    0.05      
u = mean = p =    0.09      
          
s = standard deviation = sqrt(p(1-p)/n) =    0.017102631      
          
Thus,          
          
z = (x - u) / s =    -2.338821385      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -2.338821385   ) =    0.00967234 [ANSWER]

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