A sociologist claims that children ages 12–14 spent less time sleeping in 1981 than children ages 12–14 do today. A study was conducted in 1981 to find the time that children ages 12–14 spent sleeping on weekdays. The results (in hours per weekday) are shown below. Assume the population standard deviation is 0.5 hour.
Recently, a similar study was conducted. The results are shown below. Assume the population standard deviation is 0.4 hour.
At α = 0.01, can you support the sociologist’s claim?
(a) Identify the claim and state H0, and Ha,
(b) Find the critical value(s) and identify the rejection region(s),
(c) Find the standardized test statistic z,
(d) Decide whether to reject or fail to reject the null hypothesis,
(e) Interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology.
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