SOLUTION: A random sample of 450 shoppers at Quincy Mall found that 125 favored longer shopping hours. Is this sufficient evidence at the 0.05 level of significance to conclude that less tha

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Question 1040977: A random sample of 450 shoppers at Quincy Mall found that 125 favored longer shopping hours. Is this sufficient evidence at the 0.05 level of significance to conclude that less than 30% of the shoppers at Quincy Mall favor longer hours? (Write all five steps of the significance test)
Answer by stanbon(75887) (Show Source):
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A random sample of 450 shoppers at Quincy Mall found that 125 favored longer shopping hours. Is this sufficient evidence at the 0.05 level of significance to conclude that less than 30% of the shoppers at Quincy Mall favor longer hours? (Write all five steps of the significance test)
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Ho: p >= 0.3
Ha: p < 0.3 (claim)
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sample proportion:: p-hat = 125/450 = 0.28
test statistic:: z(0.28) = (0.28-0.30)/sqrt[0.3*0.7/450] = -0.9258
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p-value = p(z < -0.9258) = normalcdf(-100,-0.9258) = 0.1773
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Since the p-value is greater than 5%, fail to reject Ho.
Conclusion:: The test results do not support the claim
that less than 30% of shoppers favor longer hours.
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Cheers,
Stan H.
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