In 2007 the National Fire Protection Association reported that 22% of all firewo

Question

In 2007 the National Fire Protection Association reported that 22% of all fireworks injuries affected the eyes. The administrator of a local hospital claims that in his community the percentage is actually higher. His ER reported 40 eye injuries in the 154 patients who presented with fireworks injuries. Test the administrator’s claim at the =0.05 level of significance. List the (a) original claim, (b) the null and hypothesis statements, (c) any critical values, (d) the test statistic, and (e) the final conclusion based on the original claim.

Please show how you got answers:)

Explanation / Answer

a) Original claim: The percentage of injuries affected the eyes is higher

b) Null hypothesis: H0: P<0.22
Alternative hypothesis H1:P>0.22

c) Z critical value at Alpha =0.05 is 1.654

d) Test statistic

Z = P - p / Sqrt(pq/n)
wherin, P=x/n =40/154 =0.259
Z = 0.259 -0.22 / Sqrt(0.22 *0.78/154)
= 1.190
Z critical value at alpha =0.05 =1.645

e) Conclusion:

Z=1.190, Z critical =1.645

Z< Z critical
Hence we accept H0, Based on original claim the percentage of injuries affected the eyes is less
  

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