Government data show that 8% of the American population are at least 75 years of

Question

Government data show that 8% 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 260 members of the households contacted, 6% are 75 years or older. (a) Is each of the boldface numbers a parameter or a statistic? 8%: statistic, 6%: parameter 8%: statistic, 6%: statistic 8%: parameter, 6%: statistic 8%: parameter, 6%: parameter (b) Assume that your county's population is similar to the American population in age distribution. What are the mean and standard deviation of the sample proportion P who are at least 75 years of age in samples of 260 respondents? (c) What is the probability that a random sample of 260 respondents would contain less than 6% of individuals at least 75 years of age? (Use 3 decimal places)

Explanation / Answer

a)

OPTION C: 8% parameter; 6% statistics [ANSWER]

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

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b)

Here,  
n =    260
p =    0.08

Hence,

u = mean = p =    0.08 [ANSWER]
  
s = standard deviation = sqrt(p(1-p)/n) =    0.01682489 [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 =    0.06      
u = mean = p =    0.08      
          
s = standard deviation = sqrt(p(1-p)/n) =    0.01682489      
          
Thus,          
          
z = (x - u) / s =    -1.188715053      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -1.188715053   ) =    0.117275907 [ANSWER]

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