# 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.

### Is a 95% confidence interval wider than a 90% confidence interval?

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).#### What does it mean to have a narrow confidence interval?

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.#### How are standard deviation and standard error related?

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.#### Is standard error the same as variance?

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.

B.

### What is the effect of increasing the level of confidence on the width of the interval?

**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".

#### What happens to the width of the confidence interval as the confidence level increases?

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).#### What happens to the margin of error if you increase the confidence level?

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**.#### Is a smaller standard error better?

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.

C.

### What is a good 95% confidence interval?

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.#### Can confidence intervals overlap and still be significant?

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.#### What is the significance of the width of the confidence interval?

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".#### What is the z score for 99 confidence interval?

Confidence IntervalsDesired Confidence Interval Z Score 90% 95% 99% 1.645 1.96 2.576

Updated: 22nd September 2018