Q: When the confidence interval is wider than a prediction interval?

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No, it is not. A 99% confidence interval would be wider. Best regards, NS

Never!

if the confidence interval is 24.4 to 38.0 than the average is the exact middle: 31.2, and the margin of error is 6.8

Yes. Simply make sure that the interval is greater than or equal to the range of the random variable.

The increase in sample size will reduce the confidence interval. The increase in standard deviation will increase the confidence interval. The confidence interval is not based on a linear function so the overall effect will require some calculations based on the levels before and after these changes. It would depend on the relative rates at which the change in sample size and change in standard deviation occurred. If the sample size increased more quickly than then standard deviation, in some sense, then the size of the confidence interval would decrease. Conversely, if the standard deviation increased more quickly than the sample size, in some sense, then the size of the confidence interval would increase.

A confidence interval, for a given probability, is the interval within which the true value may be found with that probability if the null hypothesis is true. There are two possible reasons why a confidence interval may be asymmetrical. One is that the alternative hypothesis is asymmetrical: for example, H0 is X = 5 and H1 is X > 5 (rather than X â‰ 5). The other possible reason is that the test statistic has an asymmetrical distribution. Either of these can give rise to asymmetrical CIs.

Expected value is the outcome of confidence of how probability distribution is characterized. If the expected value is greater than the confidence interval then the results are significant.

The moon is not wider than the earth. Therefore, it can not be much wider than the earth.

t-test for means

If the first derivative of a function is greater than 0 on an interval, then the function is increasing on that interval. If the first derivative of a function is less than 0 on an interval, then the function is decreasing on that interval. If the second derivative of a function is greater than 0 on an interval, then the function is concave up on that interval. If the second derivative of a function is less than 0 on an interval, then the function is concave down on that interval.

Yes, its 600km wider

Short answer, complex. I presume you're in a basic stats class so your dealing with something like a normal distribution however (or something else very standard). You can think of it this way... A confidence interval re-scales margin of likely error into a range. This allows you to say something along the lines, "I can say with 95% confidence that the mean/variance/whatever lies within whatever and whatever" because you're taking into account the likely error in your prediction (as long as the distribution is what you think it is and all stats are what you think they are). This is because, if you know all of the things I listed with absolute certainty, you are able to accurately predict how erroneous your prediction will be. It's because central limit theory allow you to assume statistically relevance of the sample, even given an infinite population of data. The main idea of a confidence interval is to create and interval which is likely to include a population parameter within that interval. Sample data is the source of the confidence interval. You will use your best point estimate which may be the sample mean or the sample proportion, depending on what the problems asks for. Then, you add or subtract the margin of error to get the actual interval. To compute the margin of error, you will always use or calculate a standard deviation. An example is the confidence interval for the mean. The best point estimate for the population mean is the sample mean according to the central limit theorem. So you add and subtract the margin of error from that. Now the margin of error in the case of confidence intervals for the mean is za/2 x Sigma/ Square root of n where a is 1- confidence level. For example, confidence level is 95%, a=1-.95=.05 and a/2 is .025. So we use the z score the corresponds to .025 in each tail of the standard normal distribution. This will be. z=1.96. So if Sigma is the population standard deviation, than Sigma/square root of n is called the standard error of the mean. It is the standard deviation of the sampling distribution of all the means for every possible sample of size n take from your population ( Central limit theorem again). So our confidence interval is the sample mean + or - 1.96 ( Population Standard deviation/ square root of sample size. If we don't know the population standard deviation, we use the sample one but then we must use a t distribution instead of a z one. So we replace the z score with an appropriate t score. In the case of confidence interval for a proportion, we compute and use the standard deviation of the distribution of all the proportions. Once again, the central limit theorem tells us to do this. I will post a link for that theorem. It is the key to really understanding what is going on here!

Soviet Union, it is considerably wider than theUnited States

Chile is very long but longer than it is wider.

A canyon is bigger and wider than a gorge.

Yes, it's 10mm wider.

A sound is a body of water between two pieces of land, and is wider than a strait. A sound is also wider than a channel.

Farmers Almanacs prediction is that Winter will be slightly milder than normal.

My prediction is that it will decay after a half-life of more than 10^30 years. That is more than a quintillion times the current age of the universe.

Yes all continents are wider in the north than the south and no one knows why.

The interval (-3, infinity).

That's the description of the interval. It means that "g" is between the numbers specified.

The foundation provides stability to the structure so it must be wider.

A penis wider than it is long

no