Question 615451: Using hypothesis testing, I am trying to solve the following question: In a survey of 300 owners of cars equipped with seat belts, 165 stated that they regularly use this equipment. The remaining 135 reported only infrequent or no use of the seatbelts. The investigator wishe to know whether this data provides sufficient evidence to indicate that fewer than 60% of the sampled population regualrly uses safety belts. Let alpha= 0.01.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In a survey of 300 owners of cars equipped with seat belts, 165 stated that they regularly use this equipment. The remaining 135 reported only infrequent or no use of the seatbelts. The investigator wishe to know whether this data provides sufficient evidence to indicate that fewer than 60% of the sampled population regularly uses safety belts. Let alpha= 0.01.
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Ho: p >= 0.6
Ha: p < 0.6 (claim)
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P-hat = 165/300 = 0.55
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z(0.55) = (0.55-0.60)/sqrt[0.6*0.4/300] = -1.7678
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p-value = P(z < -1.7678) = normalcdf(-100,-1.7678) = 0.0385
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Conclusion:
Since the p-value is greater than 1%, fail to reject Ho.
The test results do not support the claim.
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cheers,
Stan H.
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