Question

Vaccination location	No severe reaction	Severe reaction	Total
thigh	4758	30	4788
arm	8840	76	8916
Total	13598	106	13704

1 points   

QUESTION 11

1. The chi-square statistic for the table in number 10 is approximately 2.07.

   Find the corresponding test statistic  z when analyzing this data as a two-sample test of proportions, H₀:p₁=p₂ versus H_a: p₁≠p₂, using the following assignments:.

   • Let x₁ = count of those vaccinated in the thigh who had a severe reaction.
   • Let n₁ = the number vaccinated in the thigh
   • Let x₂ = count of those vaccinated in the arm who had a severe reaction
   • Let n₁ = the number vaccinated in the arm.

   You can do this, because the two tests H₀:p₁=p₂ versus H_a: p₁≠p₂, and the Chi-Square Test are equivalent for 2x2 tables.

   Give your answer to two decimal places.

2. What is the value of P-value for the test on the data in #10? (Use the output from two sample test you just did or the chi-square distribution result for the chi-square test statistic -- it will be the same either way) Give your answer to two decimal places.

3. Which of these is not a correct interpretation of the test on the table in number 10?

   	A.	Study findings are consistent with the hypothesis that vaccination site and occurrence of a severe reaction are independent.
   	B.	The proportion of children who have a severe reaction to the DTaP vaccine depends on the injection site.
   	C.	We do not have evidence of a difference in the proportions of children who have severe reactions to the vaccine when vaccinated in the arm or the thigh.
   	D.	The study found no significant association between the vaccination site (arm or thigh) and occurrence of a severe reaction.

Answer 1

Ho:   p1 - p2 =   0
Ha:   p1 - p2 ╪   0

first sample size,     n1=   4788
number of successes, sample 1 =     x1=   4758
proportion success of sample 1 , p̂1=   x1/n1=   0.993734336
      
second sample size,     n2 =    8916
number of successes, sample 2 =     x2 =    8840
proportion success of sample 1 , p̂ 2=   x2/n2 =    0.991475998
      
difference in sample proportions,    p̂1 - p̂2 =     0.002258338

      
pooled proportion , p =   (x1+x2)/(n1+n2)=   0.9923
      
std error ,SE =    =SQRT(p*(1-p)*(1/n1+ 1/n2)=   0.0016

      
Z-statistic =    (p̂1 - p̂2)/SE =    1.4387

p-value =        0.1502 [excel function =2*normsdist(-1.4387)
decision :    p-value>α,Don't reject null hypothesis

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option b) is answer

The proportion of children who have a severe reaction to the DTaP vaccine depends on the injection site.