Blood specimens taken from patients at a local clinic are routinely sent to one
ID: 3224584 • Letter: B
Question
Blood specimens taken from patients at a local clinic are routinely sent to one of two laboratories to be analyzed. The two labs have different methods for analyzing the specimens, and it is suspected that the two labs generate substantially different results. The doctors at the clinic wanted to compare the two labs, and they discussed various ways they might collect the data needed to perform a statistical test.
One doctor suggested that they take blood from 60 patients and send 30 to Lab 1 and the other 30 to Lab 2.
Another doctor objected to this idea, preferring instead to take blood from only 30 patients. The blood from each patient was divided and put into two separate vials, with one vial going to Lab 1 and one vial going to Lab 2.
The data shown here were collected according to the second doctor's recommendation. Analyze these data to determine if there is a difference between the two laboratories.
1. Identify whether or not this is a paired test.
2. State the null and alternative hypotheses.
3. Give the test statistic and the p-value.
4. Should we reject H0?
5. What is our conclusion?
Lab 1 Lab 2 79.2 82.1 80.9 81.1 81.2 80.0 81.3 81.5 81.5 81.0 82.5 82.0 82.8 83.1 82.9 76.0 83.0 82.8 83.2 82.1 83.6 81.1 83.8 79.4 83.9 82.9 84.1 80.0 85.0 82.9 85.0 89.7 85.2 89.4 85.4 86.8 85.6 85.9 85.7 84.9 86.5 86.4 86.7 83.7 87.3 84.0 87.9 85.2 88.0 83.7 88.4 84.8 88.5 85.7 89.6 88.5 84.4 89.7 90.0 89.7Explanation / Answer
1. Identify whether or not this is a paired test.
This is not the paired t-test. Here we apply two sample t-test.
2. State the null and alternative hypotheses.
below are the null and alternate hypothesis
3. Give the test statistic and the p-value.
4. Should we reject H0?
As p-value is greater than significance level of 0.05, we fail to reject the null hypothesis
5. What is our conclusion?
This means there is not sufficient evidence to conclude that there is the difference in the results from the two labs.
Null Hypothesis Alternate Hypothesis H0: 1 = 2 Ha: 1 2