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# Hypothesis Test

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The duration of human gestation is on average 40.5 weeks. In a maternity ward, we note the gestational age of 100 consecutive newborns. The sum of these ages is equal to 3850 weeks and the standard deviation is 5 weeks. We believe that it is a ward for premature births. Do we have enough evidence to support our claim? Make sure you specify the test statistic that you are using and properly formulate Ho (Null Hypothesis) and Ha (Alternate Hypothesis).

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Problem: The duration of human gestation is on average 40.5 weeks. In a maternity ward, we note the gestational age of 100 consecutive newborns. The sum of these ages is equal to 3850 weeks and the standard deviation is 5 weeks. We believe that it is a ward for premature births. Do we have enough evidence to support our claim? Make sure you specify the test statistic that you are using and properly formulate Ho and Ha.

Solution:
In the maternity ward, the mean gestational age of the newborns is given as:
Mean gestational age,x ̅=(Sum of the gestational ages of the newborns)/(Number of newborns)=3850/100=38.5
We shall have to test the claim that this maternity ward is a ward for premature births. In other words, we shall have to test the hypothesis that the mean gestational age of the newborns in ...

#### Solution Summary

The solution provides step-by-step method of performing a hypothesis test. All the steps of hypothesis testing (formulation of null and alternate hypotheses, selection of significance level, choosing the appropriate test-statistic, decision rule, calculation of test-statistic and conclusion) have been explained and the statistical analysis has been shown in details.

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