## Saturday, April 16, 2016

### Confidence infrerval for proportion example

"Many teens understand the risks of texting behind the wheel," said Amanda
Lenhart, co-author of the Pew report, "but the desire to stay connected is so strong for teens and
their parents that safety sometimes takes a back seat to staying in touch with friends and family."
Overall, 81 percent of U.S. residents use cell-phone while driving, according to the National
Highway Traffic Safety Administration. Consider a random sample of 100 U.S. residents from
which 89 admitted using cell-phones while driving.
Perform now an appropriate test hypothesis to check if the proportion of Americans who used
their cellphone while driving is significantly higher than 0.81 at 5% level.

For this problem, you need to recognize that this will be a test for proportion, so the parameter is population proportion p, then from the problem we know the hypotheses must be p = .81 and p > .81. The level of significance is given in the problem at .05. Remember that the null hypothesis always contains an equals sign. The conditions we have to see if np and n(1-p) are greater than 5. Some texts say they must be greater than 10, not sure what your book says, but either way they are both greater than 10 as well. Now we need the test statistic Z, which is p^-p divided by square root(pq/n), where q = 1-p.  Now once we have that test statistic, compare it to the critical value which we can find using the standard normal distribution chart and Z at .05 significance for right-tailed test is 1.645.