Question

A study of seat belt use involved children who were hospitalized after motor vehicle crashes. For a group of 123 children who were wearing seat belts, the number of days in intensive care units (ICU) has a mean of 0.80 and a standard deviation of 1.70. For a group of 290 children who were not wearing seat belts, the number of days spent in ICUs has a mean of 1.30 and a standard deviation of 2.06 (based on data from some recorded research findings)

a. Us a 0.05 significance level to test the claim that children wearing seat belts have a lower mean length of time in an ICU than the mean for children not wearing seat belts. [Hint: STAT -TESTS -2-SampleTTest, and then complete the required statistics]

b. Construct a confidence interval appropriate for the hypothesis test in part (a). [Hint: STAT -TESTS -2-SampTInt, and then complete the required statistics]

c. What important conclusion do the results suggest?

Answer 1

Ans:

a)

Test statistic:

t=(0.80-1.30)/sqrt((1.70^2/123)+(2.06^2/290))

t=-2.56

df=123-1=122

p-value=P(t<-2.56)=0.0058

As,p-value<0.05,we reject the null hypothesis.

b)

95% confidence interval for difference in means

=(0.8-1.30)+/-1.980*sqrt((1.70^2/123)+(2.06^2/290))

=-0.5+/-0.39

=(-0.89, -0.11)

c)There is sufficient evidence to support the claim that children wearing seat belts have a lower mean length of time in an ICU than the mean for children not wearing seat belts.