Question

A manufacturer of carpentry screws claims that its production machine is very accurate and that the standard deviation of the length of all screws produced is .08 mm or less. A sample of 30 screws showed a standard deviation of .10. The test statistic to test the manufacturer's claim is _____. a. 45.31 b. 19.2 c. 23.2 d. 18.56

Answer 1

Option (a) 45.31

Explanation:

Data provided in the question:

Standard deviation, σ = 0.08 mm

Sample size, n = 30

standard deviation of 30 samples, s = 0.10

Now,

σ² = (0.08)² = 0.0064

s² = (0.10)² = 0.01

Test Statistic = [ ( n - 1) × s²] ÷ σ²

or

Test Statistic = [ (30 - 1 ) × 0.01 ] ÷ 0.0064

= ( 29 × 0.01 ) ÷ 0.0064

= 45.31

Hence,

Option (a) 45.31