Question

#2.

• A random sample of 25 professional basketball players shows a mean height of 6 feet, 5 inches with a 95% confidence interval of 0.4 inches. Explain what this indicates.
• If the sample were smaller, would the confidence interval become smaller or larger? Explain.
• If you wanted a higher level of confidence (99%) would the confidence interval become smaller or larger? Explain.

Answer 1

A confidence interval is calculated by:

At 95% confidence level :

=1- 0,95=0.05

Now Zcrit=Z0.05/2=1.96

At 99% confidence level:

=1- 0,99=0.01

Now Zcrit=Z0.01/2=2.58

Part I

From the above confidence interval formula we can see at smaller sample size we will get larger margin of error ()and hence the confidence interval will be larger.

Part II

At larger confidence level we will get larger margin of error as we have lager critical value and hence we will get larger confidence interval.