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 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.

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.

Not enough information is given.

Accept the null hypothesis.

Solution

Since given alternative hypotehsis suggest that the test is two tailed. So for = 0.05, critical value of z is -1.96 and 1.96. Since test statistics value z=3.78 is greater than critical value 1.96 so we reject the null hypothesis. hence, option C is correct.