Question

In a recent year, the Better Business Bureau settled 75% of complaints they received. (Source: USA Today, March 2, 2009) You have been hired by the Bureau to investigate complaints this year involving computer stores. You plan to select a random sample of complaints to estimate the proportion of complaints the Bureau is able to settle. Assume the population proportion of complaints settled for the computer stores is the 0.75, as mentioned above. Suppose your sample size is 139. What is the probability that the sample proportion will be within 5 percentage points of the population proportion? (Tip: If you compute the standard error [i.e. the standard deviation of the sampling distribution], round it to 4 digits if you have to use it in later computations.) Answer = (Enter your answer as a number accurate to 4 decimal places.)

Answer #1

Solution

Given that,

p = 0.75

1 - p = 1 - 0.75 = 0.25

n = 139

= p = 0.75

[p ( 1 - p ) / n] = [(0.75 * 0.25) / 139 ] = 0.0367

P( 0.70 < < 0.80 )

= P[(0.70 - 0.75) / 0.0367 < ( - ) / < (0.80 - 0.75) / 0.0367 ]

= P(-1.36 < z < 1.36)

= P(z < 1.36) - P(z < -1.36)

Using z table,

= 0.9131 - 0.0869

= 0.8262

In a recent year, the Better Business Bureau settled 75% of
complaints they received. (Source: USA Today, March 2, 2009) You
have been hired by the Bureau to investigate complaints this year
involving computer stores. You plan to select a random sample of
complaints to estimate the proportion of complaints the Bureau is
able to settle. Assume the population proportion of complaints
settled for the computer stores is the 0.75, as mentioned above.
Suppose your sample size is 139. What...

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complaints they received. (Source: USA Today, March 2, 2009) You
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complaints to estimate the proportion of complaints the Bureau is
able to settle. Assume the population proportion of complaints
settled for the computer stores is the 0.75, as mentioned above.
Suppose your sample size is 181....

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able to settle. Assume the population proportion of complaints
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complaints they received. (Source: USA Today, March 2, 2009) You
have been hired by the Bureau to investigate complaints this year
involving computer stores. You plan to select a random sample of
complaints to estimate the proportion of complaints the Bureau is
able to settle. Assume the population proportion of complaints
settled for the computer stores is the 0.75, as mentioned above.
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complaints they received. (Source: USA Today, March 2, 2009) You
have been hired by the Bureau to investigate complaints this year
involving computer stores. You plan to select a random sample of
complaints to estimate the proportion of complaints the Bureau is
able to settle. Assume the population proportion of complaints
settled for the computer stores is the 0.75, as mentioned above.
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complaints they received. (Source: USA Today, March 2, 2009) You
have been hired by the Bureau to investigate complaints this year
involving computer stores. You plan to select a random sample of
complaints to estimate the proportion of complaints the Bureau is
able to settle. Assume the population proportion of complaints
settled for the computer stores is the 0.75, as mentioned above.
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complaints they received. (Source: USA Today, March 2, 2009) You
have been hired by the Bureau to investigate complaints this year
involving computer stores. You plan to select a random sample of
complaints to estimate the proportion of complaints the Bureau is
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settled for the computer stores is the 0.75, as mentioned above.
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complaints to estimate the proportion of complaints the Bureau is
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