CH8_9problems

CH8_9problems - A governmental survey taken from 1999-2002...

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A governmental survey taken from 1999-2002 found that the average 7 year old boy weighed 59.8 lbs and 15% of those boys were overweight. Some researchers want to see if, in the past decade, 7 year old boys have gotten heavier. They take a random sample of 150 boys and Fnd, in this random sample, that 17% are overweight. The average weight of a 7 year old boy in their sample was 61.2 lbs and the standard deviation for the weight was 13.6 lbs. A) Is there evidence that 7 year old boys, on average, are getting heavier? Remember to state your hypotheses, Fnd your test statistic, calculate your p-value, and draw your conclusions. There's a lot of data mentioned in this problem. So the best place to start with this problem is with the question: "Is there evidence that 7 year old boys, on average, are getting heavier?" Whenever you see the phrase: "Is there evidence. .." you are being asked to perform a hypothesis test. You will need to do all 4 steps. Any time you see the word "average", you know you're dealing with a quantitative variable, and your hypotheses need to be about µ . THE FOUR STEPS 1. Hypotheses: The problem asks: are 7 year old boys getting heavier? Heavier than what? The problem mentions how heavy they were, on average, in 1999-2002. So the established value, or null value, must be what they weighed a decade ago; i.e. the null value must be µ 0 = 59.8 lbs. As for the alternative, the problem does specifically state direction, which is we want to see if boys are getting heavier, or greater than, 59.8 lbs. Therefore, the Hypotheses are: Ho : µ = 59.8 lbs. Ha : µ > 59.8 lbs. 2. Test statistic: I always write down all the data from the sample before I start calculating. x = 61.2 lbs s = 13.6 lbs n = 150 Then I find the standard error (se) : se = s n = 13.6 lbs 150 = 1.11 lbs Finally, the test statistic. Since we're dealing with averages, it is best to use t. Of course, since our n=150, you can use z if you'd like, but I'll proceed with t for consistency: t = x 0 se = 61.2 lbs 59.8 lbs 1.11 lbs = 1.26 and df = 150 - 1 = 149 3. The p-value using R: > pt(1.26, 149) [1] 0.8951804 But the alternative is >, so the p value = 1- 0.895 = 0.105 (no need to double b/c one-sided) using table B: The closest degrees of freedom are either 100 or infinity. Let's use 100:
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CH8_9problems - A governmental survey taken from 1999-2002...

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