A lumber company is making boards that are 2867.02867.0 millimeters tall. If the boards are too long they must be trimmed, and if the boards are too short they cannot be used. A sample of 2525 is made, and it is found that they have a mean of 2865.82865.8 millimeters with a standard deviation of 8.08.0. A level of significance of 0.050.05 will be used to determine if the boards are either too long or too short. Assume the population distribution is approximately normal. Find the value of the test statistic. Round your answer to three decimal places.

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wifilethbridge wifilethbridge · Answer 1 · 2019-11-26T08:44:23+01:00

Answer:

-0.750

Step-by-step explanation:

A lumber company is making boards that are 2867.0 millimeters tall.

[tex]\mu = 2867.0 mm[/tex]

[tex]x = 2865.8\\s = 8[/tex]

A level of significance of 0.05

Sample size = n = 25

Since n < 30

So we will use t test

Formula : [tex]t=\frac{x-\mu}{\frac{s}{\sqrt{n}}}[/tex]

Substitute the values in the formula :

[tex]t=\frac{ 2865.8-2867.0}{\frac{8}{\sqrt{25}}}[/tex]

[tex]t=-0.750[/tex]

Hence the value of the test statistic is -0.750