Respuesta :
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 [tex]\mu[/tex] = population mean length of the board.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 2564.0 millimeters {means that the board's length is equal to 2564.0 millimeters}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 2564.0 millimeters {means that the boards are either too long or too short}
The test statistics that will be used here is One-sample t-test statistics because we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s }{\sqrt{n}} }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean length of boards = 2559.5 millimeters
s = sample standard deviation = 15.0 millimeters
n = sample of boards = 26
So, the test statistics = [tex]\frac{2559.5-2564.0}{\frac{15.0 }{\sqrt{26}} }[/tex] ~ [tex]t_2_5[/tex]
= -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 we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
Therefore, we conclude that the board's length is equal to 2564.0 millimeters.
