Math Help - stats: Confidence Interval!

-----Which of the following statements is untrue?

1)The Central Limit Theorem says that, for samples of size at least 30, the average of observations from any single distribution becomes normally distributed.

2) Confidence intervals for population proportions, constructed using z-scores as critical values, are only valid under the Central Limit Theorem.

3) Confidence intervals for population means of normal populations, constructed using z-scores as critical values, are valid even without the Central Limit Theorem

4) The Central Limit Theorem says that, for samples of size at least 30, individual observations from any distribution become normally distributed.


-----Which of the following is a true statement?

1) The width of a confidence interval for a population proportion will change from sample to sample, for a fixed confidence level.

2) The width of a confidence interval will always change from sample to sample, regardless of what we're estimating (mean or population).

3) The width of a confidence interval for a population mean will change from sample to sample, for a fixed confidence level.

4) The width of a confidence interval will never change from sample to sample, regardless of what we're estimating (mean or proportion).

5) A 90% confidence interval will be the same for every sample taken.

Originally Posted by Vedicmaths

-----Which of the following statements is untrue?

1)The Central Limit Theorem says that, for samples of size at least 30, the average of observations from any single distribution becomes normally distributed.

2) Confidence intervals for population proportions, constructed using z-scores as critical values, are only valid under the Central Limit Theorem.

3) Confidence intervals for population means of normal populations, constructed using z-scores as critical values, are valid even without the Central Limit Theorem

4) The Central Limit Theorem says that, for samples of size at least 30, individual observations from any distribution become normally distributed.

Mr F asks: Which ones do you think are untrue and why?


-----Which of the following is a true statement?

1) The width of a confidence interval for a population proportion will change from sample to sample, for a fixed confidence level.

2) The width of a confidence interval will always change from sample to sample, regardless of what we're estimating (mean or population).

3) The width of a confidence interval for a population mean will change from sample to sample, for a fixed confidence level.

4) The width of a confidence interval will never change from sample to sample, regardless of what we're estimating (mean or proportion).

5) A 90% confidence interval will be the same for every sample taken.

Mr F asks: Which ones do you think are true and why?

I'm happy to provide comment on your answers.

Some of the questions I asked at http://www.mathhelpforum.com/math-he...tion-help.html are relevant here ........

Thank you so much for offering help.
I think the statement: The Central Limit Theorem says that, for samples of size at least 30, individual observations from any distribution become normally distributed, is untrue. Individual observations from a distribution will follow that distribution. It is only the means of large samples that are covered by the Central Limit Theorem.

Actually, without some basic assumptions about the "any single distribution", I think ( The Central Limit Theorem says that, for samples of size at least 30, the average of observations from any single distribution becomes normally distributed.) would be false also...I am kinda confused!

And I think in the "true" problem:
-->A 90% confidence interval will be the same for every sample taken is true..
--> The width of a confidence interval will always change from sample to sample, regardless of what we're estimating (mean or population) is true as well. according to the formula we have:
point estimate +- (Critical value) . (standard error).

Thanks for the help!

Originally Posted by Vedicmaths

Thank you so much for offering help.
I think the statement: The Central Limit Theorem says that, for samples of size at least 30, individual observations from any distribution become normally distributed, is untrue. Individual observations from a distribution will follow that distribution. It is only the means of large samples that are covered by the Central Limit Theorem.

Mr F says: Looks fine.

Actually, without some basic assumptions about the "any single distribution", I think ( The Central Limit Theorem says that, for samples of size at least 30, the average of observations from any single distribution becomes normally distributed.) would be false also...I am kinda confused!

Mr F says: 30 is probably large enough.

And I think in the "true" problem:
-->A 90% confidence interval will be the same for every sample taken is true..

Mr F says: The width depends on sample size n ....... Does every sample have the same size ....??

--> The width of a confidence interval will always change from sample to sample, regardless of what we're estimating (mean or population) is true as well. according to the formula we have:
point estimate +- (Critical value) . (standard error).

Mr F says: How can you say they're both true? They are, more or less, the opposite of each other ....!!

Thanks for the help!

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