Answer
We can't reject the null hypothesis since -2.71 falls out of the critical region and this means that there isn't enough evidence to support the claim that the average height of buildings of 30 or more stories in a large city is at least 700 feet.
Work Step by Step
Step 1: State the hypotheses and identify the claim.
$$H_0: \mu =700\\H_1: \mu \gt 700$$
Step 2: Find the critical value(s).
$$ At \ \alpha = 0.025 \ and\ d.f. = 9, \ the \ critical\ value\ is\ 2.262 $$
Step 3: Find the test value.
$$ \bar x= \frac{485+511+...+616+582}{10}=\frac{6065}{10}=606.5$$
$$s^2= \frac{\sum (x- \bar x)^2}{n-1}= \frac{ (485- 606.5)^2+(511- 606.5)^2+...+(582- 606.5)^2}{9}=11898.28\\
s=\sqrt{s^2}=\sqrt{11898.28}=109.079$$
$$t=\frac{\bar x −μ}{\frac{s}{\sqrt{n}}} = \frac{606.5−700}{\frac{109.079}{\sqrt{10}}} ≈ -2.71\\$$
Step 4: Make the decision.
we can't reject the null hypothesis since -2.71 falls out of the critical region.
Step 5: Summarize the results.
There isn't enough evidence to support the claim that the average height of buildings of 30 or more stories in a large city is at least 700 feet.
