Binomial distribution help!

Which of the following statements is true? pick 4 possible statements!

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) The Central Limit Theorem says that, for samples of size at least 30, the average of observations from any single distribution becomes normally distributed.
6) Confidence intervals for population proportions, constructed using z-scores as critical values, are only valid under the Central Limit Theorem.
7) Confidence intervals for population means of normal populations, constructed using z-scores as critical values, are valid even without the Central Limit Theorem.
8) The Central Limit Theorem says that, for samples of size at least 30, individual observations from any distribution become normally distributed.
9) The sample used for creating a confidence interval for a population proportion must have at least 30 observations, regardless of the number of successes.
10) A 90% confidence interval will be the same for every sample taken.
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Thanks!

Quote:

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Originally Posted by Vedicmaths

Which of the following statements is true? pick 4 possible statements!

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).

Mr F wonders: (Thinking) Does the confidence interval depend on sample size n .......? (Thinking)

5) The Central Limit Theorem says that, for samples of size at least 30, the average of observations from any single distribution becomes normally distributed.
6) Confidence intervals for population proportions, constructed using z-scores as critical values, are only valid under the Central Limit Theorem.
7) Confidence intervals for population means of normal populations, constructed using z-scores as critical values, are valid even without the Central Limit Theorem.
8) The Central Limit Theorem says that, for samples of size at least 30, individual observations from any distribution become normally distributed.

Mr F ponders: (Thinking) What is the statement of the Central Limit Theorem? How large is large ......? (Thinking)

9) The sample used for creating a confidence interval for a population proportion must have at least 30 observations, regardless of the number of successes.

Mr F muses: (Thinking) Can you construct a confidence interval for a sample of size n = 20 ....? (Thinking)

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

Mr F contemplates: (Thinking) Does the confidence interval depend on sample size n .......? Is every sample taken always the same size .....? (Thinking)
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Thanks!

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