# Hypothesis testing and confidence intervals

• Mar 3rd 2011, 09:26 AM
jhallett17
Hypothesis testing and confidence intervals
Here is the question:
Suppose that we are interested in buying ball bearings from a certain manufacturer. We require very precisely manufactured ball bearings, and so we decide to investigate this manufacturer's output. The manufacturer insists that at least 98% of their manufactured bearings will be within our acceptable tolerance limits.
We decide to test this claim. Let's test the claim that the population proportion that are within tolerance limits is .98, against the alternative that the true proportion is less than .98.
Suppose we draw a random sample of 1000 of the ball bearings, and find only 912 are within the acceptable tolerance limits.

#15. What is a 95% confidence interval for the proportion of bearings that are within tolerance limits?
A) .912 ± .018
B) .912 ± .021
C) .912 ± .024
D) .912 ± .027
E) .912 ± .030

#16. Which one of the following represents the appropriate hypotheses?
A) Ho: p=.98 Ha: p>.98
B) Ho: p-hat =.98 Ha: p-hat <.98
C) Ho: p=.98 Ha: p doesn't equal .98
D) Ho: p=.98 Ha: p<.98

I don't understand how you can do them without standard deviation. Some help in starting the question would be great.
• Mar 3rd 2011, 02:53 PM
matheagle
use $\displaystyle \hat p \pm Z_{\alpha/2}\sqrt{{\hat p\hat q\over n}}$

where z=1.96

The st deviation of $\displaystyle \hat p$ is $\displaystyle \sqrt{{pq\over n}}$
and you don't know p or q, so you estimate them.