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In: Statistics and Probability

There are three (3) cases for handling the comparison of means using the Student’s t-test. For...

There are three (3) cases for handling the comparison of means using the Student’s t-test. For each of the scenarios listed below, identify which case (i.e. Case #1, #2, or #3) you would use in order to determine if the results agree “within experimental error”: Provide a brief explanation to receive full credit!

  1. A FDA scientist is testing a sample of ground beef, suspected of being contaminated with E-Coli, using one of their standard methods. The average of several replicated measurements of the ground beef are compared to a national standard with a known high E-Coli count.
  1. An EPA scientist measures the amount of nitrate ion (NO3−) in both rainwater and unchlorinated drinking water by both gas chromatography and spectrophotometry.
  1. A CDC scientist wants to compare replicate concentration measurements of a white powder (suspected of being anthrax, found in an envelope) using Methods 2A and 4C.
  1. You have completed your training at an environmental research laboratory. To insure that you are ready to work on your own, your supervisor wants to compare your results of an oil contaminated water analysis to that of an in-house standard sample.

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Expert Solution

The three cases for handling the comparison of means using student's t-test are:

Case #1: One sample t-test: This test is conducted when there is only one sample and will be compared with a population mean

Case #2: Independent sample t-test: This test is conducted to compared means of two groups but when both groups are independent of each other

Case# 3: Paired sample test: This test is conducted to compared means of two groups but when both groups are dependent on each other

a. An FDA scientist is testing a sample of ground beef, suspected of being contaminated with E-Coli, using one of their standard methods. The average of several replicated measurements of the ground beef is compared to a national standard with a known high E-Coli count.

Answer: Case #1: One sample t-test

b. An EPA scientist measures the amount of nitrate ion (NO3−) in both rainwater and unchlorinated drinking water by both gas chromatography and spectrophotometry.

Answer: Case #2: Independent sample t-test

c. A CDC scientist wants to compare replicate concentration measurements of a white powder (suspected of being anthrax, found in an envelope) using Methods 2A and 4C.

Answer: Case# 3: Paired sample test

d. You have completed your training at an environmental research laboratory. To insure that you are ready to work on your own, your supervisor wants to compare your results of an oil-contaminated water analysis to that of an in-house standard sample.

Answer: Case #1: One sample t-test

orchestra answered 2 years ago
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