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Answer:
We conclude that the board's length is equal to 2564.0 millimeters.
Step-by-step explanation:
We are given that a sample of 26 is made, and it is found that they have a mean of 2559.5 millimeters with a standard deviation of 15.0.
Let = <u><em>population mean length of the board</em></u>.
So, Null Hypothesis, :
= 2564.0 millimeters {means that the board's length is equal to 2564.0 millimeters}
Alternate Hypothesis, :
2564.0 millimeters {means that the boards are either too long or too short}
The test statistics that will be used here is <u>One-sample t-test statistics</u> because we don't know about the population standard deviation;
T.S. = ~
where, = sample mean length of boards = 2559.5 millimeters
s = sample standard deviation = 15.0 millimeters
n = sample of boards = 26
So, <em><u>the test statistics</u></em> = ~
= -1.529
The value of t-test statistics is -1.529.
Now, at a 0.05 level of significance, the t table gives a critical value of -2.06 and 2.06 at 25 degrees of freedom for the two-tailed test.
Since the value of our test statistics lies within the range of critical values of t, so <u><em>we have insufficient evidence to reject our null hypothesis</em></u> as it will not fall in the rejection region.
Therefore, we conclude that the board's length is equal to 2564.0 millimeters.