Homework SourseThe amount of time Americans spend watching television is cl
The amount of time Americans spend watching television is closely monitored by A.C. Nielsen because this helps to determine advertising pricing for commercials. It is known the distribution of time Americans watch television is right skewed, with a mean of 2.35 hours per day and a standard deviation of 1.93 (Sullivan, pp. 440).
a. (1 pt.) If a random sample of 4 Americans was taken, what would be the mean, standard deviation and shape of the distribution of sample means?
b. (1 pt.) If a random sample of 100 Americans was taken, what would be the mean, standard deviation and shape of the distribution of sample means?
c. (1 pt.) Is the mean of the distribution of sample means greater than, equal to, or less than the original population mean?
d. (1 pt.) Is the standard deviation of the distribution of sample means greater than, equal to, or less than the original population standard deviation?
e. (1 pt.) If we have a large enough sample size, what rule, theorem, or law allows us to assume that the sampling distribution of means is approximately normal?
f. (1 pt.) What is the probability that a random sample of 100 Americans results in a mean hours of television watched in a day to be below 2 hours a day?
Solution
a)
It would be bell shaped, according to the central limit theorem.
It will have the same mean, ux = 2.35.
The standard deviation of it is sigma/sqrt(n) = 1.93/sqrt(4) = 0.965 [answer]
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b)
It would be bell shaped, according to the central limit theorem.
It will have the same mean, ux = 2.35.
The standard deviation of it is sigma/sqrt(n) = 1.93/sqrt(100) = 0.193 [answer]
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c)
It is EQUAL.
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d)
IT IS LESS THAN, as we divide the original standard deviation by sqrt(n).
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