Respuesta :
Answer:
There is not enough evidence to support the claim that the doors are either too long or too short.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 2058.0 millimeters
Sample mean, [tex]\bar{x}[/tex] = 2047.0 millimeters
Sample size, n = 17
Alpha, α = 0.10
Sample standard deviation, s = 27
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 2058.0\text{ millimeter}\\H_A: \mu \neq 2058.0\text{ millimeter}[/tex]
We use Two-tailed t test to perform this hypothesis.
Formula:
[tex]t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }[/tex]
Putting all the values, we have
[tex]t_{stat} = \displaystyle\frac{ 2047.0 - 2058.0}{\frac{27}{\sqrt{17}} } = -1.6798[/tex]
Now, [tex]t_{critical} \text{ at 0.10 level of significance, 16 degree of freedom } = \pm 1.7396[/tex]
Since, the calculated t statistic lies in the acceptance region, we fail to reject the null hypothesis and accept the null hypothesis.
Thus, there is not enough evidence to support the claim that the doors are either too long or too short.