Question

A lab technician is tested for her consistency by taking multiple measurements of cholesterol levels from the same blood sample. The target accuracy in the past has been 2.5 or less with a standard deviation of 1.15. If the lab technician takes 16 measurements and the variance of the measurements in the sample is 2.2, does this provide enough evidence to reject the claim that the lab technician’s accuracy is within the target accuracy?

At the a = .05 level of significance, what is your conclusion?

• A.

  Reject H₀. At the  alpha= .05 level of significance, there is not enough evidence to support the claim that this technician’s true average is less than the target accuracy.

• B.

  Cannot determine

• C.

  Reject H₀ . At the   = .05 level of significance, there is enough evidence to support the claim that this technician’s average is less than the target accuracy.

• D.

  Do not reject H₀. At the  = .05 level of significance there is not sufficient evidence to suggest that this technician’s true average is less than the target accuracy.

Answer 1

Answer:

Given,

Ho : = 2.5

Ha : < 2.5

test statistic = (n-1)*s^2/^2

substitute values

= (16-1)*2.2/2.5^2

= 5.28

Here alpha = 0.05, degree of freedom = n-1 = 16-1 = 15

critical chi square value = 7.261 [since from chi square table]

Here we observe that,

test statistic < critical value, so we fail to reject Ho.

So there is no sufficient evidence.

Do not reject H₀. At the  = .05 level of significance there is not sufficient evidence to suggest that this technician’s true average is less than the target accuracy.