Question

A lumber company is making boards that are 2920.0 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 12 is made, and it is found that they have a mean of 2922.7 millimeters with a variance of 121.00. A level of significance of 0.05 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.

Answer 1

The value of the test statistic is of 0.22.

Explanation:

Our test statistic is:

`t = (X - \mu)/((\sigma)/(√(n)))`

In which X is the sample mean,
`\mu` is the expected mean,
`\sigma` is the standard deviation(square root of the variance) and n is the size of the sample.

A lumber company is making boards that are 2920.0 millimeters tall.

This means that
`\mu = 2920`.

A sample of 12 is made, and it is found that they have a mean of 2922.7 millimeters with a variance of 121.00.

This means that
`X = 2922.7, n = 12, \sigma = √(121) = 11`. So

`t = (X - \mu)/((\sigma)/(√(n)))`

`t = (2922.7 - 2922)/((11)/(√(12)))`

`t = 0.22`

The value of the test statistic is of 0.22.