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Sagot :
Answer:
Due to the test statistic, there is sufficient evidence to support the claim that the doors are too short.
Step-by-step explanation:
The null hypothesis is:
[tex]H_{0} = 2058[/tex]
The alternate hypotesis is:
Since the sample mean is less than the expected mean, we test the
[tex]H_{1} < 2058[/tex]
Our test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
A lumber company is making doors that are 2058.0 millimeters tall.
This means that [tex]\mu = 2058[/tex]
A sample of 25 is made, and it is found that they have a mean of 2043.0 millimeters with a standard deviation of 6.0.
This means, respectively, that [tex]n = 25, \mu = 2043, \sigma = 6[/tex]
Test statistic:
[tex]z = \frac{2043 - 2058}{\frac{6}{\sqrt{25}}}[/tex]
[tex]z = -12.5[/tex]
Looking at the z-table, z = -12.5 has a pvalue of 0 < 0.1, which means that there is sufficient evidence to support the claim that the doors are too short.
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