SOLUTION: In a recent study of 86 random teenagers in Utah, the mean number of hours per week that they played video games was 21.6 with σ=5.7 hours. a.) State and verify the requirement

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Question 1140864: In a recent study of 86 random teenagers in Utah, the mean number of hours per week that they played video games was 21.6 with σ=5.7 hours.
a.) State and verify the requirements for a valid confidence interval. Then find and report the 95% confidence interval estimating the mean number of hours per week that teenagers in Utah play video games. (Please state the calculator option you used. Round to one decimal place).
b.) Larry, a statistics student, uses the above CI to estimate the mean number of hours per week that American teenagers played video games. Would the estimate be valid? Justify.
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
it would be the mean+/-1.96 (the z-value for 95% middle of distribution)*sigma/sqrt(n)
this is 21.6+/-1.96(5.7)/sqrt(86); the half-interval is 1.20
the interval is therefore (20.4, 22.8). Used the formula and checked with calculator "Z-interval" because the SD of sigma implies a population. If one meant s, the sd of the sample, it needs to be labelled such.
then t is used with 1.99 as the value and the half-interval changes to 1.22, although the final interval to the nearest tenth would still be the same using "T interval." The notation is important.
The interval is a sample of Utah teenagers, not Americans. It is therefore valid for the population in Utah. It might be appropriate for Americans in general, but that requires Utahns being a reasonable sample of Americans, which is not likely.