Question

A lumber company is making boards that are 2563.02563.0 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 1515 is made, and it is found that they have a mean of 2560.52560.5 millimeters with a standard deviation of 8.08.0. A level of significance of 0.10.1 will be used to determine if the boards are either too long or too short. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the boards are either too long or too short?

Answer

2 Points

Keypad

There is not sufficient evidence to support the claim that the boards are either too long or too short. There is sufficient evidence to support the claim that the boards are either too long or too short.

Answer 1

Given that, sample size (n) = 15

sample mean = 2560.5 millimetres and

sample standard deviation = 8.0

The null and alternative hypotheses are,

H0 : μ = 2563.0

Ha : μ ≠ 2563.0

Test statistic is,

Degrees of freedom = 15 - 1 = 14

t-critical values at significance level of 0.1 are, t^* = ± 1.761

Since, test statistic = -1.210 > -1.761, we fail to reject the null hypothesis.

Conclusion : There is not sufficient evidence to support the claim that the boards are either too long or too short.