SOLUTION: This is not in a textbook - Can you please help?? Let us assume that average gas prices per gallon of unleaded gasoline in U.S. are normally distributed with the mean of $2.89 a

Question 130021: This is not in a textbook - Can you please help??
Let us assume that average gas prices per gallon of unleaded gasoline in U.S. are normally distributed with the mean of $2.89 and the standard deviation of $0.05. Your neighborhood gas station charges $3.13 per gallon. You suspect the station owner charges too much and wish to determine whether there is a statistically significant difference between his price and the national average. Perform the z-test of hypothesis on the 0.05 level of significance. What is the conclusion?
Answer by stanbon(48568) (Show Source):
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Let us assume that average gas prices per gallon of unleaded gasoline in U.S. are normally distributed with the mean of $2.89 and the standard deviation of $0.05. Your neighborhood gas station charges $3.13 per gallon. You suspect the station owner charges too much and wish to determine whether there is a statistically significant difference between his price and the national average. Perform the z-test of hypothesis on the 0.05 level of significance. What is the conclusion?
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Ho:mu = 2.89
Ha: mu > 2.89
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Critical value for one-tail z-test and alpha = 5%: z = 1.645
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Test statistic:
z(3.13) = (3.13-2.89)/[0.05] = 4.8
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Sice the test statistic is greater than the critical value,
Reject Ho. There is significant statistical evidence that the
local gas station is overcharging.
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Cheers,
Stan H.