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Q: What happens to the confidence interval as the mean decreases?

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A confidence interval of x% is an interval such that there is an x% probability that the true population mean lies within the interval.

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

Never!

Confidence intervals may be calculated for any statistics, but the most common statistics for which CI's are computed are mean, proportion and standard deviation. I have include a link, which contains a worked out example for the confidence interval of a mean.

The formula for margin of error is (Z*)*(Standard Deviation))/(sqrt(N)), so as N increases, the margin of error decreases. Here N went from 100 to 5000, so N has increased by 4900. This means the margin of error decreases. Since the confidence interval is the mean plus or minus the margin of error, a smaller margin of error means that the confidence interval is narrower.

What percentage of times will the mean (population proportion) not be found within the confidence interval?

No. For instance, when you calculate a 95% confidence interval for a parameter this should be taken to mean that, if you were to repeat the entire procedure of sampling from the population and calculating the confidence interval many times then the collection of confidence intervals would include the given parameter 95% of the time. And sometimes the confidence intervals would not include the given parameter.

The Confidence Interval is a particular type of measurement that estimates a population's parameter. Usually, a confidence interval correlates with a percentage. The certain percentage represents how many of the same type of sample will include the true mean. Therefore, we would be a certain percent confident that the interval contains the true mean.

You probably mean the confidence interval. When you construct a confidence interval it has a percentage coverage that is based on assumptions about the population distribution. If the population distribution is skewed there is reason to believe that (a) the statistics upon which the interval are based (namely the mean and standard deviation) might well be biased, and (b) the confidence interval will not accurately cover the population value as accurately or symmetrically as expected.

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

Confidence interval considers the entire data series to fix the band width with mean and standard deviation considers the present data where as prediction interval is for independent value and for future values.

Confidence intervals may be calculated for any statistics, but the most common statistics for which CI's are computed are mean, proportion and standard deviation. I have include a link, which contains a worked out example for the confidence interval of a mean.

The mean plus or minus 2.576 (4/sqr.rt. 36)= 1.72 So take your average plus or minus 1.72 to get your confidence interval

For normally distributed data. One standard deviation (1σ)Percentage within this confidence interval68.2689492% (68.3% )Percentage outside this confidence interval31.7310508% (31.7% )Ratio outside this confidence interval1 / 3.1514871 (1 / 3.15)

Variance, t-value, sample mean

Mean plus or minus 1.95 SEM. Mean minus 1,95 SEM to Man plus 1,95 SEM.

normal distribution

Typically, the mean is the center and the interval extends a fixed number of standard-errors-of-the mean in wither direction. M+/- 1 SEM for example. I guess because you don't know, I should give you the simplest.

It means that 95% of the values in the data set falls within 2 standard deviations of the mean value.

1.96

1.0966

The margin of error is dependent on the confidence interval.I'll give you examples to understand it better.We know:Confidence Interval (CI) = x(bar) ± margin of error (MOE)MOE = (z confidence)(sigma sub x bar, aka standard error of mean)When CI = 95%, MOE = (1.96)(sigma sub x bar)When CI = 90%, MOE = (1.64)(sigma sub x bar)Naturally, the margin of error will decrease as confidence level decreases.

That is with a confidence interval of approximately 95% the "true mean" is within the interval of [336.10, 353.90] and that the sample mean (which is an estimate of the "true mean") is $350.00. SMALL-SAMPLE CONFIDENCE INTERVAL FOR A POPLATION MEAN, t-DISTRIBUTION 95% Confidence Interval = x-bar +/- (t-critical value) * s/SQRT(n) x-bar = SAMPLE MEAN [350] s = STANDARD DEVIATION [100] n = NUMBER OF SAMPLES [200] n - 1 = 199 df (DEGREES OF FREEDOM) t-critical value = (approx) 1.972 from "look-up Table for "two-sided interval" df = 200 [CLOSED df IN TABLE] 95% Confidence Interval: 350+/- 1.972 *100 / SQRT(200) = [336.10, 353.90] That is with a confidence interval of approximately 95% the "true mean" is within the interval of [336.10, 353.90] and that the sample mean (which is an estimate of the "true mean") is $350.00. c. ANSWER: A random selection of 1537 customers will provide 95% confidence for estimating the mean extended warranty price paid. Why??? CHOOSING THE SAMPLE SIZE n = [(z-critical value * s)/B]^2 z-critical value = 1.96 (associated with 95% confidence level) s = STANDARD DEVIATION [100.00] B = BOUND ON THE ERROR OF ESTIMATION [5.00] n = [(1.96 * 100.00)/5.00]^2 = 1537 (ROUNDED - UP) CONCLUSION: A random selection of 1537 customers will provide 95% confidence for estimating the mean extended warranty price paid.

The graph moves to the left.

It means something that happens once in a while. Something with an irregular interval of happening.