STATISTICS 8.1, 8.2.
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Does the population need to be normally distributed for the sampling distribution of x
overbar to be approximately normally distributed? Why? - Answer: No because the
Central Limit Theorem states that regardless of the shape of the underlying population,
the sampling distribution of x overbar becomes approximately normal as the sample
size, n, increases.
What effect does increasing the sample size have on the probability? Provide an
explanation for this result. - Answer: Increasing the sample size decreases
Why is the sampling distribution of x overbar approximately normal? - Answer: If a
random variable X is normally distributed, the distribution of the sample mean, x over
bar, is normally distributed. If the sample size is large enough, n greater than or equals
30, the sampling distribution is approximately normal regardless of the shape of the
population.
The sampling distribution of x overbar is approximately normal because the sample size
is large enough.
Without doing any computation, decide which has a higher probability, assuming each
sample is from a population that is normally distributed with ri equals 100
And sigma equals 15.
Explain your reasoning. - Answer: Both probabilities are based on a sample from the
same population. The only difference is the sample size. The sampling distribution of
the mean becomes narrower as the sample size is increased. Since the given interval,
90 less than or equal x less than or equals110,
Contains the mean of 100, then more of the sampling distribution is contained in the
interval as the sample size is increased. That means that the probability increases as
the sample size increases.
1
APPHIA - Crafted with Care and Precision for Academic Excellence.
Quality content you can rely on!
Does the population need to be normally distributed for the sampling distribution of x
overbar to be approximately normally distributed? Why? - Answer: No because the
Central Limit Theorem states that regardless of the shape of the underlying population,
the sampling distribution of x overbar becomes approximately normal as the sample
size, n, increases.
What effect does increasing the sample size have on the probability? Provide an
explanation for this result. - Answer: Increasing the sample size decreases
Why is the sampling distribution of x overbar approximately normal? - Answer: If a
random variable X is normally distributed, the distribution of the sample mean, x over
bar, is normally distributed. If the sample size is large enough, n greater than or equals
30, the sampling distribution is approximately normal regardless of the shape of the
population.
The sampling distribution of x overbar is approximately normal because the sample size
is large enough.
Without doing any computation, decide which has a higher probability, assuming each
sample is from a population that is normally distributed with ri equals 100
And sigma equals 15.
Explain your reasoning. - Answer: Both probabilities are based on a sample from the
same population. The only difference is the sample size. The sampling distribution of
the mean becomes narrower as the sample size is increased. Since the given interval,
90 less than or equal x less than or equals110,
Contains the mean of 100, then more of the sampling distribution is contained in the
interval as the sample size is increased. That means that the probability increases as
the sample size increases.
1
APPHIA - Crafted with Care and Precision for Academic Excellence.
