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Heavy children: Are children heavier now than they were in the past? The National Health and Nutrition Examination Survey (NHANES) taken between 1999 and 2002 reported that the mean weight of six-year-old girls in the United States was 49.3 pounds. Another NHANES survey, published in 2008, reported that a sample of 190 six-year-old girls weighed between 2003 and 2006 had an average weight of 46 pounds. Assume the population standard deviation is =σ17 pounds. Can you conclude that the mean weight of six-year-old girls in 2006 is different from what it was in 2002? Use the =α0.10 level of significance and the critical value method.

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cchilabert

Answer:

Step-by-step explanation:

Hello!

You have two surveys that measure the weight of six-year-old girls in the USA,

1) 1999-2002

μ= 49.3 pounds

(I'll take this mean as the population value since it can be considered "historical data" or point of comparison to make the test.)

2)2003-2006

sample n= 190

sample mean x[bar]= 46 pounds

population standard deviation σ= 17 pounds

Assuming that the study variable X" Weight of six-year-old girls between 2003 - 2006" (pound) has a normal distribution.

If you need to test that the children are heavier now (2003-2006) than in the past (1999-2002) the test hypothesis is:

H₀: μ ≤ 49.3

H₁: μ > 49.3

α: 0.10

The statistic is Z= (x[bar]-μ)   ~N(0;1)

                                (δ/√n)

The critical region is one-tailed to the right.

[tex]Z_{1-\alpha } = Z_{0.90} = 1.28[/tex]

So you'll reject the null hypothesis if the calculated statistic is equal or greater than 1.28.

Z=  46 - 49.3 = -2.67

     17/√190

Since the calculated value -2.67 is less than 1.28 you do not reject the null hypothesis. In other words, the six-year-old girls from 2003-2006 are thinner than the girls from 1999-2002.

I hope it helps!

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