How to find sampling distribution of a sample mean - AP Statistics
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Which of the following is a sampling distribution?
Which of the following is a sampling distribution?
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The correct answer is the distribution of average height statistics that could happen from all possible samples of college students. Remember that a sampling distribution isn't just a statistic you get form taking a sample, and isn't just a piece of data you get from doing sampling. Instead, a sampling distribution is a distribution of sample statistics you could get from all of the possible samples you might take from a given population.
The correct answer is the distribution of average height statistics that could happen from all possible samples of college students. Remember that a sampling distribution isn't just a statistic you get form taking a sample, and isn't just a piece of data you get from doing sampling. Instead, a sampling distribution is a distribution of sample statistics you could get from all of the possible samples you might take from a given population.
Assume you have taken 100 samples of size 64 each from a population. The population variance is 49.
What is the standard deviation of each (and every) sample mean?
Assume you have taken 100 samples of size 64 each from a population. The population variance is 49.
What is the standard deviation of each (and every) sample mean?
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The population standard deviation =
The sample mean standard deviation =
The population standard deviation =
The sample mean standard deviation =
A random variable has an average of 
with a standard deviation of 
. What is the probability that out of the sample set the variable is less than 
. The sample set is 
. Round your answer to three decimal places.
A random variable has an average of
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There are two keys here. One, we have a large sample size since 
, meaning we can use the Central Limit Theorem even if points per game is not normally distributed.
Our 
-score thus becomes...
where 
is the specified points or less needed this season,
is the average points per game of the previous season,
is the standard deivation of the previous season,
and 
is the number of games.
There are two keys here. One, we have a large sample size since
Our
where
and
Reaction times in a population of people have a standard deviation of 
milliseconds. How large must a sample size be for the standard deviation of the sample mean reaction time to be no larger than 
milliseconds?
Reaction times in a population of people have a standard deviation of
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Use the fact that 
.
Alternately, you can use the fact that the variance of the sample mean varies inversely by the square root of the sample size, so to reduce the variance by a factor of 10, the sample size needs to be 100.
Use the fact that
Alternately, you can use the fact that the variance of the sample mean varies inversely by the square root of the sample size, so to reduce the variance by a factor of 10, the sample size needs to be 100.
A machine puts an average of 
grams of jelly beans in bags, with a standard deviation of 
grams. 
bags are randomly chosen, what is the probability that the mean amount per bag in the sampled bags is less than 
grams.
A machine puts an average of
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A sample size of 
bags means that the central limit theorem is applicable and the distribution can be assumed to be normal. The sample mean would be 
and 
Therefore,
A sample size of
Therefore,
If a sampling distribution for samples of college students measured for average height has a mean of 70 inches and a standard deviation of 5 inches, we can infer that:
If a sampling distribution for samples of college students measured for average height has a mean of 70 inches and a standard deviation of 5 inches, we can infer that:
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We can infer that roughly 68% of random samples of college students will have a sample mean of between 65 and 75 inches. Anytime we try to make an inference from a sampling distribution, we have to keep in mind that the sampling distribution is a distribution of samples and not a distribution about the thing we're trying to measure itself (in this case the height of college students). Also, remember that the empirical rules tells us that roughly 68% of the distribution will fall within one standard deviation of the mean.
We can infer that roughly 68% of random samples of college students will have a sample mean of between 65 and 75 inches. Anytime we try to make an inference from a sampling distribution, we have to keep in mind that the sampling distribution is a distribution of samples and not a distribution about the thing we're trying to measure itself (in this case the height of college students). Also, remember that the empirical rules tells us that roughly 68% of the distribution will fall within one standard deviation of the mean.
The standard deviation of a sampling distribution is called:
The standard deviation of a sampling distribution is called:
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The standard error (SE) is the standard deviation of the sampling distribution.
The standard error (SE) is the standard deviation of the sampling distribution.
Suppose that the mean height of college students is 70 inches with a standard deviation of 5 inches. If a random sample of 60 college students is taken, what is the probability that the sample average height for this sample will be more than 71 inches?
Suppose that the mean height of college students is 70 inches with a standard deviation of 5 inches. If a random sample of 60 college students is taken, what is the probability that the sample average height for this sample will be more than 71 inches?
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First check to see if the Central Limit Theorem applies. Since n > 30, it does. Next we need to calculate the standard error. To do that we divide the population standard deviation by the square-root of n, which gives us a standard error of 0.646. Next, we calculate a z-score using our z-score formula:
Plugging in gives us:
Finally, we look up our z-score in our z-score table to get a p-value.
The table gives us a p-value of,
First check to see if the Central Limit Theorem applies. Since n > 30, it does. Next we need to calculate the standard error. To do that we divide the population standard deviation by the square-root of n, which gives us a standard error of 0.646. Next, we calculate a z-score using our z-score formula:
Plugging in gives us:
Finally, we look up our z-score in our z-score table to get a p-value.
The table gives us a p-value of,
Which of the following is a sampling distribution?
Which of the following is a sampling distribution?
Tap to see back →
The correct answer is the distribution of average height statistics that could happen from all possible samples of college students. Remember that a sampling distribution isn't just a statistic you get form taking a sample, and isn't just a piece of data you get from doing sampling. Instead, a sampling distribution is a distribution of sample statistics you could get from all of the possible samples you might take from a given population.
The correct answer is the distribution of average height statistics that could happen from all possible samples of college students. Remember that a sampling distribution isn't just a statistic you get form taking a sample, and isn't just a piece of data you get from doing sampling. Instead, a sampling distribution is a distribution of sample statistics you could get from all of the possible samples you might take from a given population.
Assume you have taken 100 samples of size 64 each from a population. The population variance is 49.
What is the standard deviation of each (and every) sample mean?
Assume you have taken 100 samples of size 64 each from a population. The population variance is 49.
What is the standard deviation of each (and every) sample mean?
Tap to see back →
The population standard deviation =
The sample mean standard deviation =
The population standard deviation =
The sample mean standard deviation =
A random variable has an average of with a standard deviation of . What is the probability that out of the sample set the variable is less than . The sample set is . Round your answer to three decimal places.
A random variable has an average of
Tap to see back →
There are two keys here. One, we have a large sample size since , meaning we can use the Central Limit Theorem even if points per game is not normally distributed.
Our -score thus becomes...
where is the specified points or less needed this season,
is the average points per game of the previous season,
is the standard deivation of the previous season,
and is the number of games.
There are two keys here. One, we have a large sample size since
Our
where
and
Reaction times in a population of people have a standard deviation of milliseconds. How large must a sample size be for the standard deviation of the sample mean reaction time to be no larger than milliseconds?
Reaction times in a population of people have a standard deviation of
Tap to see back →
Use the fact that .
Alternately, you can use the fact that the variance of the sample mean varies inversely by the square root of the sample size, so to reduce the variance by a factor of 10, the sample size needs to be 100.
Use the fact that
Alternately, you can use the fact that the variance of the sample mean varies inversely by the square root of the sample size, so to reduce the variance by a factor of 10, the sample size needs to be 100.
A machine puts an average of grams of jelly beans in bags, with a standard deviation of grams. bags are randomly chosen, what is the probability that the mean amount per bag in the sampled bags is less than grams.
A machine puts an average of
Tap to see back →
A sample size of bags means that the central limit theorem is applicable and the distribution can be assumed to be normal. The sample mean would be and
Therefore,
A sample size of
Therefore,
If a sampling distribution for samples of college students measured for average height has a mean of 70 inches and a standard deviation of 5 inches, we can infer that:
If a sampling distribution for samples of college students measured for average height has a mean of 70 inches and a standard deviation of 5 inches, we can infer that:
Tap to see back →
We can infer that roughly 68% of random samples of college students will have a sample mean of between 65 and 75 inches. Anytime we try to make an inference from a sampling distribution, we have to keep in mind that the sampling distribution is a distribution of samples and not a distribution about the thing we're trying to measure itself (in this case the height of college students). Also, remember that the empirical rules tells us that roughly 68% of the distribution will fall within one standard deviation of the mean.
We can infer that roughly 68% of random samples of college students will have a sample mean of between 65 and 75 inches. Anytime we try to make an inference from a sampling distribution, we have to keep in mind that the sampling distribution is a distribution of samples and not a distribution about the thing we're trying to measure itself (in this case the height of college students). Also, remember that the empirical rules tells us that roughly 68% of the distribution will fall within one standard deviation of the mean.
The standard deviation of a sampling distribution is called:
The standard deviation of a sampling distribution is called:
Tap to see back →
The standard error (SE) is the standard deviation of the sampling distribution.
The standard error (SE) is the standard deviation of the sampling distribution.
Suppose that the mean height of college students is 70 inches with a standard deviation of 5 inches. If a random sample of 60 college students is taken, what is the probability that the sample average height for this sample will be more than 71 inches?
Suppose that the mean height of college students is 70 inches with a standard deviation of 5 inches. If a random sample of 60 college students is taken, what is the probability that the sample average height for this sample will be more than 71 inches?
Tap to see back →
First check to see if the Central Limit Theorem applies. Since n > 30, it does. Next we need to calculate the standard error. To do that we divide the population standard deviation by the square-root of n, which gives us a standard error of 0.646. Next, we calculate a z-score using our z-score formula:
Plugging in gives us:
Finally, we look up our z-score in our z-score table to get a p-value.
The table gives us a p-value of,
First check to see if the Central Limit Theorem applies. Since n > 30, it does. Next we need to calculate the standard error. To do that we divide the population standard deviation by the square-root of n, which gives us a standard error of 0.646. Next, we calculate a z-score using our z-score formula:
Plugging in gives us:
Finally, we look up our z-score in our z-score table to get a p-value.
The table gives us a p-value of,
Assume you have taken 100 samples of size 64 each from a population. The population variance is 49.
What is the standard deviation of each (and every) sample mean?
Assume you have taken 100 samples of size 64 each from a population. The population variance is 49.
What is the standard deviation of each (and every) sample mean?
Tap to see back →
The population standard deviation =
The sample mean standard deviation =
The population standard deviation =
The sample mean standard deviation =
A random variable has an average of with a standard deviation of . What is the probability that out of the sample set the variable is less than . The sample set is . Round your answer to three decimal places.
A random variable has an average of
Tap to see back →
There are two keys here. One, we have a large sample size since , meaning we can use the Central Limit Theorem even if points per game is not normally distributed.
Our -score thus becomes...
where is the specified points or less needed this season,
is the average points per game of the previous season,
is the standard deivation of the previous season,
and is the number of games.
There are two keys here. One, we have a large sample size since
Our
where
and
Reaction times in a population of people have a standard deviation of milliseconds. How large must a sample size be for the standard deviation of the sample mean reaction time to be no larger than milliseconds?
Reaction times in a population of people have a standard deviation of
Tap to see back →
Use the fact that .
Alternately, you can use the fact that the variance of the sample mean varies inversely by the square root of the sample size, so to reduce the variance by a factor of 10, the sample size needs to be 100.
Use the fact that
Alternately, you can use the fact that the variance of the sample mean varies inversely by the square root of the sample size, so to reduce the variance by a factor of 10, the sample size needs to be 100.
A machine puts an average of grams of jelly beans in bags, with a standard deviation of grams. bags are randomly chosen, what is the probability that the mean amount per bag in the sampled bags is less than grams.
A machine puts an average of
Tap to see back →
A sample size of bags means that the central limit theorem is applicable and the distribution can be assumed to be normal. The sample mean would be and
Therefore,
A sample size of
Therefore,