The Iowa Department of Transportation repaired hundreds of b

The Iowa Department of Transportation repaired hundreds of bridges in 1993. To check the average cost to repair a bridge, a random sample ofn = 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.

The hypothesis to be tested is:
H0: mu=25003 vs. Ha: mu not equal to 25003
The test statistic is z=3.78

Please state the correct decision?

Fail to reject the null hypothesis.

Reject the null hypothesis.

Accept the null hypothesis.

Not enough information is given.

Solution

p value for z<=3.78 is 0.00003( by using normal distribution calculator)

as it is two tailed p=2(0.00003)=0.00006<0.05(given alpha)

AS p<alpha (significance level) reject null hypothesis

option B is right