Question

Hepatitis C is a blood-borne infection with potentially serious consequences. Identification of social and environmental risk factors is important because Hepatitis C can go undetected for years after infection. A study conducted in Texas in 1991-2 examined whether the incidence of hepatitis C was related to whether people had tattoos and where they obtained their tattoos. Data were obtained from existing medical records of patients who were being treated for conditions that were not blood-related disorders. The patients were classified according to hepatitis C status (whether they had it or not) and tattoo status (tattoo from tattoo parlour, tattoo obtained elsewhere, or no tattoo). The data are summarised in the following table.
Tattoo? Has Hep C No Hep C Tattoo (parlour) 17 43 Tattoo (elsewhere) 8 54 No tattoo 22 461 (a) In any association between hepatitis C status and tattoo status, which variable would be the explanatory variable? Justify your answer. [2] (b) If a simple random sample is not available, a sample may be treated as if it was randomly selected provided that the sampling process was unbiased with respect to the research question. On the information provided above, and for the purposes of investigating a possible relation between tattoos and hepatitis C, is it reasonable to treat the data as if it was randomly selected? Briefly discuss. [2] (c) Assuming that any concerns about data collection can be resolved, evaluate the evidence that hepatitis C status and tattoo status are related in the relevant population. If you conclude that there is a relationship, describe it. Use a 1% significance level.

Answer 1

Observed = Oi	Hep C	No Hep C	Total
Tattoo (parlour)	17	43	60
Tattoo (elsewhere)	8	54	62
No tattoo	22	461	483
totals	47	558	605

Expected frequency of a cell = sum of row*sum of column / total sum

Expected	Hep C	No Hep C
Tattoo (parlour)	47*60/605= 4.66	558*60/605= 55.34
Tattoo (elsewhere)	47*62/605= 4.82	558*62/605= 57.18
No tattoo	47*483/605= 37.52	558*483/605= 445.48

Expected Count = Ei	Hep C	No Hep C
Tattoo (parlour)	4.66	55.34
Tattoo (elsewhere)	4.82	57.18
No tattoo	37.52	445.48

Chi square =(Oi-Ei)^2/Ei	Hep C	No Hep C
Tattoo (parlour)	32.68	2.75
Tattoo (elsewhere)	2.1	0.18
No tattoo	6.42	0.54
		44.67

• Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   44.658                          
                                
  Level of Significance =   0.01                          
  Number of Rows =   3                          
  Number of Columns =   2                          
  Degrees of Freedom=(#row - 1)(#column -1) = (3- 1 ) * ( 2- 1 ) =   2                          
                                
  p-Value =   0.0000   [Excel function: =CHISQ.DIST.RT(χ²,df) ]                      
  Decision:    p-value < α , Reject Ho          

  It can be concluded that there is an association   between two variables.

  Hepatitis status---Explanatory

  b)

  We can data is reasonable unbiased as expected frequency is greater than 5

  c)

    
                                
  p-Value =   0.0000   [Excel function: =CHISQ.DIST.RT(χ²,df) ]                      
  Decision:    p-value < α , Reject Ho          

• ======================================================

• If you need any clarification please let me know through comment
       Please give positive vote if you find this solution helpful. Thank you!