11.13 Review

Find the 95% confidence interval for the true proportion of U.S. girls, age 12 - 19, who have been pregnant.

The report also stated that the results of the survey are accurate to within ± 3.7% at the 95% confidence level. Suppose that a new study is to be done. It is desired to be accurate to within 2% of the 95% confidence level. What is the minimum number that should be surveyed?

Given: $X$ ~ $\text{Exp}\left(\frac{1}{3}\right)$ . Sketch the graph that depicts: $P\left(x>1\right)$ .

60% of individuals keep their cars at most how many years?

Suppose that we randomly survey one person. Find the probability that person keeps his/her car less than 2.5 years.

If we are to pick individuals 10 at a time, find the distribution for the mean car length ownership.

If we are to pick 10 individuals, find the probability that the sum of their ownership time is more than 55 years.

For which distribution is the median not equal to the mean?

• A Uniform
• B Exponential
• C Normal
• D Student-t

Compare the standard normal distribution to the student-t distribution, centered at 0. Explain which of the following are true and which are false.

• a As the number surveyed increases, the area to the left of -1 for the student-t distribution approaches the area for the standard normal distribution.
• b As the degrees of freedom decrease, the graph of the student-t distribution looks more like the graph of the standard normal distribution.
• c If the number surveyed is 15, the normal distribution should never be used.

Explain why we cannot determine the distribution of $X$ .

If you were to create a confidence interval or perform a hypothesis test for the population mean checking account balance of 20-year old college students, what distribution would you use?

Find the 95% confidence interval for the true mean checking account balance of a twenty-year-old college student.