Answer:
We conclude that the average cost to repair a bridge is greater than $25,003.
Step-by-step explanation:
We are given that to check the average cost to repair a bridge, a random sample of n = 55 bridges were 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.
Let
= <u><em>average cost to repair a bridge.</em></u>
So, Null Hypothesis,
:
$25,003 {means that the average cost to repair a bridge is smaller than or equal to $25,003}
Alternate Hypothesis,
:
> $25,003 {means that the average cost to repair a bridge is greater than $25,003}
The test statistics that would be used here <u>One-sample t-test statistics</u> as we don't know about population standard deviation;
T.S. =
~ ![t_n_-_1](https://tex.z-dn.net/?f=t_n_-_1)
where,
= sample mean cost to repair a bridge = $25,788
s = sample standard deviation = $1,540
n = sample of bridges = 55
So, <u><em>the test statistics</em></u> =
~ ![t_5_4](https://tex.z-dn.net/?f=t_5_4)
= 3.78
The value of t test statistic is 3.78.
<u>Now, at 5% significance level the t table gives critical value of 1.674 at 54 degree of freedom for right-tailed test.</u>
Since our test statistic is more than the critical value of t as 3.78 > 1.674, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which <u>we reject our null hypothesis.</u>
Therefore, we conclude that the average cost to repair a bridge is greater than $25,003.