# 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".

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).#### Why are some confidence intervals wider?

Apparently a narrow**confidence interval**implies that there is a smaller chance of obtaining an observation within that**interval**, therefore, our accuracy is higher. Also a 95%**confidence interval**is narrower than a 99%**confidence interval**which is**wider**. The 99%**confidence interval**is more accurate than the 95%.#### What does it mean when the confidence interval is negative?

The 95%**confidence interval**is providing a range that you are 95% confident the true difference in**means**falls in. Thus, the CI**can**include**negative**numbers, because the difference in**means**may be**negative**.#### What do standard error bars tell you?

**Error bars**are graphical representations of the variability of data and used on graphs to**indicate**the**error**or uncertainty in a reported measurement. They give a general idea of how precise a measurement is, or conversely, how far from the reported value the true (**error**free) value might be.

B.

### 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.#### Which confidence interval is wider?

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 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 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**.

C.

### 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.

#### 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).#### 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.#### 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.

Updated: 3rd December 2019