Young children in the United States are exposed to an average of 4 hours of back
ID: 3156042 • Letter: Y
Question
Young children in the United States are exposed to an average of 4 hours of background television per day (CNN website, November 13, 2012). Having the television on in the background while children are doing other activities may have adverse consequences on a child's well-being. You have a research hypothesis that children from low-income families are exposed lo more than 4 hours of daily background television. In order to test this hypothesis, you have collected information from a random sample of 60 children from low income families and found that these children were exposed to a sample mean of 4 5 hours of daily background television. Develop hypotheses that can be used to test your research hypothesis. Based on a previous study, you are willing to assume that the population standard deviation is sigma = 0.5 hours. What is the p-value based on your sample of 60 children from low-income families? Use alpha =.01 as the level of significance. What is your conclusion?Explanation / Answer
a)
Formulating the null and alternative hypotheses,
Ho: u <= 4
Ha: u > 4 [ANSWER]
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b)
As we can see, this is a right tailed test.
Getting the test statistic, as
X = sample mean = 4.5
uo = hypothesized mean = 4
n = sample size = 60
s = standard deviation = 0.5
Thus, z = (X - uo) * sqrt(n) / s = 7.745966692
Also, the p value is
p = 4.74287*10^-15 [ANSWER]
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c)
As P < 0.01, we REJECT THE NULL HYPOTHESIS.
Hence, there is significant evidence that children from low-income families are exposed to more than 4 hours of daily background television. [CONCLUSION]
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