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Mailings ReviewView nces nless you need to edit, it's safer to stay in Protected View. Enable Editing 2. A study of seat belt use Involved children who were hospitalized after motor vahicle 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 0.83 and a standard deviation of 1.77. For a group of 290 children who wers not wearing seat belts, the number of days spent in ICUs has a mean of 1.39 and a standard deviation of 3.06 (based on data from "Morbidity Among Pediatric Motor vehicle Crash Victims: The effectiveness of Seat Belts," by osberg and Di Scala, American Journal of Public Health, vol. 82, No. 3). a Test the claim using a hypothesis test. Use a o.o5 significance level to test the claim that children wearing set belts have a lower mean length of time in the ICU than the mean for children not wearing seat belts. In Statcrunch click on Stat T Stats > Two-samplex with Summary. compute. (Leave pooled variance off Pill in your information and click State your null and aiternative hypothesis State your t-Stat State your P-value e . Do you "reject or "Fail to Reject the nuli hypothesis b. Test the claim by constructing a 90% confidence interval. If you had just completed part a you can click options at the top and then edit, to change your information for part b. otherwise follow the steps below. in statcrunch click on Stati T Stats > Two-5ample with summary Fil in your information, then click the box that shows Confidence interval and put in your confidence level and ciick compute Give the lower and upper values of your confidence interval t eased on your answers to part a and b what 42 the resuts snggett?

Explanation / Answer

a) The StatCrunch output for this problem is:

Two sample T summary hypothesis test:
1 : Mean of Population 1
2 : Mean of Population 2
1 - 2 : Difference between two means
H0 : 1 - 2 = 0
HA : 1 - 2 < 0
(without pooled variances)

Hypothesis test results:

Hence,

Null and Alternative hypotheses:

H0 : 1 - 2 = 0
HA : 1 - 2 < 0

t - stat = -2.33

P - value = 0.0102

Since p - value is less than significance level 0.05, we reject the null hypothesis.

b) StatCrunch output for 90% confidence interval is:

Two sample T summary confidence interval:
1 : Mean of Population 1
2 : Mean of Population 2
1 - 2 : Difference between two means
(without pooled variances)

90% confidence interval results:

Hence,

Lower limit = -0.956

Upper limit = -0.164

c) Since p - value is less than 0.05 and confidence interval does not include 0, we reject the null hypothesis.

Hence,

We have sufficient evidence to conclude that Children wearing seat belts have a lower mean length of time in the ICU than the mean of Children not wearing seat belts.

Difference Sample Diff. Std. Err. DF T-Stat P-value 1 - 2 -0.56 0.24033104 373.79013 -2.3301193 0.0102

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