Question

A surveying company decides to base a portion of their employees’ salary raises on improvement in their use of equipment. To determine the improvement, the employees measure their ability to point on a target and read the circles of a theodolite every six months. One employee is tested six weeks after starting employment and obtains a standard deviation of ±1.6” with 30 measurements. Six months later the employee obtains a standard deviation of ±1.3” with 35 measurements. Did the employee improve statistically over six months at a 5% level of significance? Is this test an acceptable method of determining improvements in quality? What suggestion, if any, would you give to modify the test?

Answer 1

Answer:

Given,

Null hypothesis

Ho : σ_A² < σ_B²

Alternative hypothesis

H_A: σ_A² > σ_B²

n1 = 30

n2 = 35

DF1 = n1 - 1

= 30 - 1

= 29

DF2 = n2 - 1

= 35 - 1

= 34

Test statistic = F = s1^2/s2^2

substitute values

= 1.6^2 / 1.3^2

F = 1.515

Here it is right tailed test

So the corresponding p value for F distribution is 0.124

Here p value > significance level(0.05) , so we fail to reject the null hypothesis Ho.

So we can say that there is insufficient evidence to conclude that the employee improve statistically over six months at a 5% level of significance.