Question

A lumber company is making boards that are 2932.0 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 18 is made, and it is found that they have a mean of 2933.5 millimeters with a standard deviation of 13.0 . A level of significance of 0.1 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

Step 1:

Null hypothesis states that the length of the board is equal to 2932.0 millimeters

Ho :   = 2932.0 millimeters

Ha : 2932.0 millimeters

Step 2: Test Statistics

Population mean = = 2932.0 millimetres

sample size = n = 18

sample mean = = 2933.5 millimetres

sample deviation = s = 13.0 millimeters

level of significance = 0.1

Population is normally distributed. Since the sample size is less than 30 and population standard deviation is not given use T statistics.

Step 3:

The t-critical values for a two-tailed test, for a significance level of =0.1 are

Graphically

As t statistics does not fall in the rejection region we fail to reject the null hypothesis