Our children heavier now than they were in a pass the national health and nutrition examination survey taken at 1:19 99 and 2002 reported that the main white of six-year-old girls in the United States was 49.3 pounds another survey published in 2008 reported that a sample of 196-year-old girl wide between 2003 and 2006 for the average way to 47.5 pounds assume the population standard deviation is 14 pounds

Answer:

Since the calculated value -1.8 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.

Step-by-step explanation

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= 196

sample mean x[bar]= 47.5 pounds

population standard deviation σ= 14 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:

H?: μ ≤ 49.3

H?: μ > 49.3

α: 0.10

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

The critical region is one-tailed to the right.

Z_1-α = Z_{1-0.10 =} Z_{0.90 = 1.28}

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

Z= (47.5 - 49.3)/(14/√196)  = -1.8