Factor V is a protein involved in the forming of blood clots. The higher the level of factor V, the faster the blood clots. A Blood Transfusions Service is interested in the effects of sterilization of blood plasma because factor V is unstable and may break down during sterilization. The table below gives measured levels of factor V in blood samples from nine donors. Both pre- and post-sterilization measurements are given for each person. Test whether the mean factor V levels are different post-sterilization. Run the test at a 5% level of significance. Give each of the following  1) the appropriate null and alternative hypotheses; 2) the appropriate test; 3) the decision rule; 4) the calculation of the test statistic; and 5) your conclusion including a comparison to alpha or the critical value. Factor V measurementsDonor numberPre-SterilizationPost-Sterilization110259852106010303953923484789257506506855759794782889788849899809

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Asked Oct 22, 2019
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Factor V is a protein involved in the forming of blood clots. The higher the level of factor V, the faster the blood clots. A Blood Transfusions Service is interested in the effects of sterilization of blood plasma because factor V is unstable and may break down during sterilization. The table below gives measured levels of factor V in blood samples from nine donors. Both pre- and post-sterilization measurements are given for each person. Test whether the mean factor V levels are different post-sterilization. Run the test at a 5% level of significance. Give each of the following  1) the appropriate null and alternative hypotheses; 2) the appropriate test; 3) the decision rule; 4) the calculation of the test statistic; and 5) your conclusion including a comparison to alpha or the critical value. 

Factor V measurements

Donor number
Pre-Sterilization
Post-Sterilization
1
1025
985
2
1060
1030
3
953
923
4
847
892
5
750
650
6
855
759
7
947
828
8
978
884
9
899
809
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Expert Answer

Step 1

(1)

Here, the claim of the test is that the mean factor V levels are different post-sterilization.

The test hypotheses are given below:

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Null hypothesis: H 4=0 Alternative hypothesis: H 40

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Step 2

(2)

In matched-pair design, the subjects are paired according to particular characteristics after which a subject is assigned to a treatment group and another subject.

Here, the samples are dependent. Hence, paired t test is appropriate.

(3)

Rejection rule:

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Step 3

(4)

Step-by-step procedure to obtain the test statistic and p-value using Excel:

  • In Excel sheet, enter Pre-Sterilization in one column and enter Post-Sterilization in one column.
  • In Data, select Data Analysis and choose t-test; Paired Two Samples for Means.
  • In Input Variable 1 Range, select Pre-Sterilization.
  • In Input Variable 2 Range, select Post-Sterilization.
  • In Hypothesized Mean D...
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t-Test: Paired Two Sample for Means Pre-Sterilization Post-Sterilization 862.2222222 Мean 923.7777778 Variance 9321.694444 13496.94444 Observations 9 Pearson Correlation 0.896614355 Hypothesized Mean Difference df 8 tStat 3.550935525 P(T<=t) one-tail 0.003749599 tCritical one-tail 1.859548038 P(T<t) two-tail 0.007499197 t Critical two-tail 2.306004135

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