Answer
We can't reject the null hypothesis because there isn't enough evidence to support the claim that the average cost of teeth straightening with metal braces is less than 5400.
Work Step by Step
Step 1: State the hypotheses and identify the claim.
$$H_0: \mu =5400\\H_1: \mu \lt 5400$$
Step 2: Find the critical value(s).
$$ At \ \alpha = 0.025 \ and\ d.f. = 27, \ the \ critical\ value\ is\ -2.052 $$
Step 3: Find the test value.
$$t=\frac{\bar x −μ}{\frac{s}{\sqrt{n}}} = \frac{5250−5400}{\frac{629}{\sqrt{28}}} ≈ -1.26\\$$
Step 4: Make the decision.
We can't reject the null hypothesis since -1.26 falls out of the critical region.
Step 5: Summarize the results.
There isn't enough evidence to support the claim that the average cost of teeth straightening
with metal braces is less than 5400.
