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11 what can we conclude about the alternative

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Unformatted text preview: ision for 3 hours or more on a given day. The mean sleep duration for this sample was 6.78 hours with a standard deviation of 0.63 hours. The second sample has the sleep durations of 18 children who watched television for less than 3 hours on a given day. The mean sleep duration for this sample was 7.44 hours with a standard deviation of 1.05 hours. Researchers have carefully examined these populations and determined that we may assume that they are normal. Can we conclude at the 5% level of significance that children who watch more than 3 hours of television get less sleep than children who watch less than 3 hours of television? Step 1: Determine the hypotheses 1 Assuming that the children who watch 3 hours or more are population 1 and children who watch less than 3 are population 2, state the null and alternative hypotheses. 2 Will this be a left ­tailed, right ­tailed, or two ­tailed test? Step 2: Collect the data 3 Are the approximate normality criteria met for each sampling distribution? 4 Are the samples independent? 5 Calculate the difference of sample means, !! − !! 6 Is the difference of sample means consistent with your alternative hypothesis? © 2011 THE CARNEGIE FOUNDATION FOR THE ADVANCEMENT OF TEACHING A PATHWAY THROUGH STATISTICS, VERSION 1.6, STATWAY™  ­ STUDENT HANDOUT STATWAY™ STUDENT HANDOUT | 10 Lesson 10.4.1 Inference from Independent Samples Step 3: Assess the Evidence 7 Calculate the test statistic for the observed mean of sample differences. 8 Sketch the T ­distribution and identify the position of the observed test statistic. Shade the area that represents the P ­value. 9 Find the P ­value. In this situation there are 28 degrees of freedom for the T ­distribution. Step 4: State a Conclusion 10 How does the P ­value compare to the significance level? Should we reject or fail to reject the null hypothesis? 11 What can we conclude about the alternative hypothesis? 12 State a conclusion in the context of the problem. Now that we know a difference exists, we want to know how large the difference is. To estimate the difference, we can find a confidence interval. © 2011 THE CARNEGIE FOUNDATION FOR THE ADVANCEMENT OF TEACHING A PATHWAY THROUGH STATISTICS, VERSION 1.6, STATWAY™  ­ STUDENT HANDOUT STATWAY™ STUDENT HANDOUT | 11 Lesson 10.4.1 Inference from Independent Samples 13 Determine the...
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