In an experiment to determine whether there is a systematic difference between the weights obtained with two different mass balances, six specimens were weighed, in grams, on each balance. The following data
Were obtained: Compute the test statistic.
A) 1.083
B) 2.433
C) 2.666
D) 0.313

Question

In an experiment to determine whether there is a systematic difference between the weights obtained with two different mass balances, six specimens were weighed, in grams, on each balance. The following data
Were obtained:  Compute the test statistic.
A) 1.083 
B) 2.433 
C) 2.666 
D) 0.313

Quizplus · Accepted Answer

To test whether there is a systematic difference between the weights obtained with two different mass balances, we can use a paired t-test. The test statistic for a paired t-test is given by:

t = (mean difference) / (standard deviation of the differences / sqrt(n))

From the given data, we can calculate the mean difference and standard deviation of the differences as follows:

Mean difference = (-0.002 + 0.023 + 0.009 + 0.015 + 0.018 + 0.019) / 6 = 0.015

Standard deviation of differences = sqrt[((-0.002 - 0.015)^2 + (0.023 - 0.015)^2 + (0.009 - 0.015)^2 + (0.015 - 0.015)^2 + (0.018 - 0.015)^2 + (0.019 - 0.015)^2) / (6 - 1)] = 0.013

Plugging in these values, we get:

t = 0.015 / (0.013 / sqrt(6)) = 2.666

Therefore, the test statistic is 2.666. The best choice is C.

In an Experiment to Determine Whether There Is a Systematic