A study in Pediatric Emergency Care compared the injury seve

A study in Pediatric Emergency Care compared the injury severity between younger and older children. One measure reported was the Injury Severity Score (ISS). The standard deviation of ISS scores for 32 children 8 years or younger was 23.4, and the standard deviation for 45 children older than 8 years was 6.5. Assume that ISS scores are normally distributed for both age groups. At the 0.01 level of significance, is there sufficient reason to conclude that the standard deviation of ISS scores for younger children is larger than the standard deviation of ISS scores for older children?

(a) Find F. (Give your answer correct to two decimal places.)

(ii) Find the p-value. (Give your answer correct to four decimal places.)

(b) State the appropriate conclusion

Solution

H0: sigma 1 = sigma 2

Ha: sigma 1 > sigma 2

s1 = 23.4

s2 = 6.5

F=s1^2/s2^2

= 12.96

df = 31. 44

p value = 0.00

As p < 0.01, reject null hypothesis

Accept alternate hypothesis.

There sufficient reason to conclude that the standard deviation of ISS scores for younger children is larger than the standard deviation of ISS scores for older children