SOLUTION: a radio manufacturer claims that 65% of teenagers 13 to 16 years old have their own portable radios. A researcher wishes to test the claim and selects a random sample of 80 teeage

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Question 290754: a radio manufacturer claims that 65% of teenagers 13 to 16 years old have their own portable radios. A researcher wishes to test the claim and selects a random sample of 80 teeagers.She finds that 57 have their own portable radios. at a=0.05 sould the claim be rejected?use te P=value method.
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Answer by stanbon(75887) About Me  (Show Source):
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a radio manufacturer claims that 65% of teenagers 13 to 16 years old have their own portable radios. A researcher wishes to test the claim and selects a random sample of 80 teeagers.She finds that 57 have their own portable radios. at a=0.05 sould the claim be rejected?use te P=value method.
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Ho: p = 0.65 (claim)
Ha: p is not equal to 0.65
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sample proportion: 57/80 = 0.71
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test statistic: z(0.71) = (0.71-0.65)/sqrt[0.65*0.35/80[ = 1.1720
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p-value = 2*P(z>1.1720) = 0.2412
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Conclusion: Since the p-value is greater than 5%, fail to reject Ho.
The test results support the manufacturer's claim.
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Cheers,
Stan H.