How can the width of a confidence interval be reduced?
- Increase the sample size. Often, the most practical way to decrease the margin of error is to increase the sample size.
- Reduce variability. The less that your data varies, the more precisely you can estimate a population parameter.
- Use a one-sided confidence interval.
- Lower the confidence level.
A 99 percent confidence interval would be wider than a 95 percent confidence interval (for example, plus or minus 4.5 percent instead of 3.5 percent). A 90 percent confidence interval would be narrower (plus or minus 2.5 percent, for example).
- A 95% confidence interval is a range of values that you can be 95% certain contains the true mean of the population. With large samples, you know that mean with much more precision than you do with a small sample, so the confidence interval is quite narrow when computed from a large sample.
- A: The standard deviation, or SD, measures the amount of variability or dispersion for a subject set of data from the mean, while the standard error of the mean, or SEM, measures how far the sample mean of the data is likely to be from the true population mean. The SEM is always smaller than the SD.
- The standard deviation of the mean (SD) is the most commonly used measure of the spread of values in a distribution. SD is calculated as the square root of the variance (the average squared deviation from the mean). The spread of a distribution is also referred to as dispersion and variability.
Increasing the sample size decreases the width of confidence intervals, because it decreases the standard error. c) The statement, "the 95% confidence interval for the population mean is (350, 400)", is equivalent to the statement, "there is a 95% probability that the population mean is between 350 and 400".
- The width of the confidence interval decreases as the sample size increases. The width increases as the standard deviation increases. The width increases as the confidence level increases (0.5 towards 0.99999 - stronger). The width increases as the significance level decreases (0.5 towards 0.0000001 - stronger).
- Answer: As sample size increases, the margin of error decreases. As the variability in the population increases, the margin of error increases. As the confidence level increases, the margin of error increases.
- If you measure a sample from a wider population, then the average (or mean) of the sample will be an approximation of the population mean. The smaller the standard error, the less the spread and the more likely it is that any sample mean is close to the population mean. A small standard error is thus a Good Thing.
If repeated samples were taken and the 95% confidence interval was computed for each sample, 95% of the intervals would contain the population mean. A 95% confidence interval has a 0.95 probability of containing the population mean. 95% of the population distribution is contained in the confidence interval.
- When 95% confidence intervals for the means of two independent populations don't overlap, there will indeed be a statistically significant difference between the means (at the 0.05 level of significance). However, the opposite is not necessarily true.
- Increasing the sample size decreases the width of confidence intervals, because it decreases the standard error. c) The statement, "the 95% confidence interval for the population mean is (350, 400)", is equivalent to the statement, "there is a 95% probability that the population mean is between 350 and 400".
- Confidence Intervals
Desired Confidence Interval Z Score 90% 95% 99% 1.645 1.96 2.576
Updated: 2nd October 2019