8/19/2019 Inference in Two Means

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8/19/2019 Inference in Two Means

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2. [ liverloberatio.sav]  A hepatologist is interested to determine if the left-to-right lobe liver ratio of patients withcirrhosis differ with patients with normal liver. Using 17 sonograph images of different patients (9 normapatients and 8 cirrhotic patients), diameters were recorded and left-to-right liver ratio were computed. Themean left-to-right liver ratio of normal patients is 0.8607 (SD = 0.11487) and 1.2756 (SD = 0.19208) forcirrhotic patients. Do the data provide sufficient evidence that patients with cirrhosis have significantly highermean left-to-right lobe liver ratio as compared to normal patients? Test at ! = 0.05.

Hypotheses:

Ho: _____________________________________________________________________________________Ha: _____________________________________________________________________________________

 Test statistic: _____________  p-value: ___________________

Critical value: _____________

Decision: _____________

Conclusion: _________________________________________________________________________________  

3. [dengueplt.sav]  A group of researchers wanted to determine if the mean platelet counts of patients diagnosed with dengue fever is significantly less than those diagnosed with Chikungunya fever. Twenty seven patients oeach group participated and results are as follows:

 At 5% level of significance, do the data provide sufficient evidence that themean platelet counts of patients diagnosed with dengue fever is significantly lessthan those diagnosed with Chikungunya fever?

Hypotheses:Ho: _____________________________________________________________________________________

Ha: _____________________________________________________________________________________

 Test statistic: _____________  p-value: ___________________

Critical value: _____________

Decision: _____________

Conclusion: _________________________________________________________________________________

Fever Mean SD t stat p-value

Dengue 55.1852 16.0489Chikungunya 271.7407 76.9148

8/19/2019 Inference in Two Means

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4. [dengueplt2.sav] Suppose same group of researchers (as discussed in item # 3) wanted to determine if otherCBC parameters (WBC, RBC, Hematocrit, & Hemoglobin) of patients diagnosed with dengue are significantlyless with those diagnosed with chikungunya.

 Actual SPSS outputs: 

 Table 1. CBC Parameters of Dengue and Chikungunya Patients Parameters Dengue Chikungunya t stat p-value

 WBC (x109 /L) 5.73 ± 0.59 6.35 ± 0.45 0.827 0.206RBC (x1012 /L) 4.49 ± 0.13 4.84 ± 0.07 2.319 0.013HCT 0.38 ± 0.01 0.39 ± 0.01 1.113 0.137HGB (g/L) 126.78 ± 4.33 130.93 ± 1.98 0.871 0.195

Values expressed as mean ± SEM, n = 27.

Statement of the results:

 There is sufficient evidence that the mean RBC count [t37.9 = 2.319, p = 0.013] of patients diagnosed

 with Chikingunya fever is significantly less those diagnosed with dengue fever. This indicates that the mean

RBC count of patients diagnosed with dengue is less by 0.34 x1012 /L (CI95%: 0.04 to 0.64).

No sufficient evidence was found that the mean WBC count (t52 = 0.827, 

 p = 0.103), hematocrit (t35 =

1.113,  p  = 0.137) and hemoglobin (t36.4 = 0.871,  p  = 0.195) of patients diagnosed with dengue fever and

Chikingunya fever differ.

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5.  [smokersCBC.sav ] Suppose that in example 1, segmenters, hemoglobin and hematocrit were also measuredComplete the table below and state your conclusion. Test at 5% level of significance.

 Table 2. Segmenter, Hemoglobin, and Hematocrit of Smokers and Non-smokers

ParametersSmokers(n=43)

Non-smokers(n=45) t stat  p-value

Segmenters (%) 0.53 ± 0.02 *0.50 ± 0.01Hemoglobin (g/L) 153.07 ± 3.19 134.44 ± 2.09

Hematocrit 0.407 ± 0.006 0.400 ± 0.003Values expressed as mean ± SEM.

 p-values are based on independent t-test.

* p<0.05 : the mean segmenter (%) is significantly below the normal range.

 Normal reference values used were: 0.55 to 0.70% for segmenters; 122 to 162 g/L for hemoglobin; and 0.36 to 0.49 for hematocrit.

Statement of the results:

 ___________________________________________________________________________________ 

 ___________________________________________________________________________________ 

 ___________________________________________________________________________________ 

 ___________________________________________________________________________________ 

 ___________________________________________________________________________________ 

 ___________________________________________________________________________________ 

Inference in Two Dependent Means (Paired t-test)determines if the changes in the observations has 2P I Q 

!   !!!!!!!!

!

  df = n – 1

Example: [fitnripe.sav] Fit ‘n Ripe is a product, which enables the costumers tolose their body weight (in lbs) after two weeks, along with proper diet and exercise. A random sample of 9 costumers took the product and their body weightsdecreased as shown in the table below. At a = 0.05, is there sufficient evidence thatthe product is effective in losing customer’s body weight after two weeks?

Hypotheses:Ho: _____________________________________________________________

Ha: _____________________________________________________________

 Test statistic: _____________  p-value: ___________________

Critical value: _____________

Decision: _____________

Conclusion: _________________________________________________________________________________