The Iowa Department of Transportation repaired hundreds of bridges in 1993. To c
ID: 3376258 • Letter: T
Question
The Iowa Department of Transportation repaired hundreds of bridges in 1993. To check the average cost to repair a bridge, a random sample of n = 55 bridges was chosen. The mean and standard deviation for the sample are $25,788 and $1,540, respectively. Records from previous years indicate an average bridge repair cost was $25,003. Use the sample data to test that the 1993 mean ? is greater than $25,003. Use ? = 0.05.
What type of test would be used?
Z test difference between two means
T test difference between two means
T test
Z test
A.Z test difference between two means
B.T test difference between two means
C.T test
D.Z test
Explanation / Answer
C. T test
Here we are not comparing between two means, we are testing whether the population mean equals to a specified value ($25,003) or greater than that. So this is a single sample problem. Note that the sample standard deviation is given, not the population standard deviation. Assuming normality one can perform one-sample T test. Even if we do not assume that the sample comes from normal distribution, due to large sample size (n=55) we can use asymptotic normality and hence we perform Z test.
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