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The next two questions refer to the following real study:
A recent survey of U.S. teenage pregnancy was answered by 720 girls, age 12 - 19. 6% of the girls surveyed said they have been pregnant. ( Parade Magazine ) We are interested in the true proportion of U.S. girls, age 12 - 19, who have been pregnant.
Find the 95% confidence interval for the true proportion of U.S. girls, age 12 - 19, who have been pregnant.
$\left(0\text{.}\text{0424},0\text{.}\text{0770}\right)$
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?
2401
Given: $X$ ~ $\text{Exp}\left(\frac{1}{3}\right)$ . Sketch the graph that depicts: $P\left(x>1\right)$ .
The next four questions refer to the following information:
Suppose that the time that owners keep their cars (purchased new) is normally distributed with a mean of 7 years and a standard deviation of 2 years. We are interested in how long an individual keeps his car (purchased new). Our population is people who buy their cars new.
60% of individuals keep their cars at most how many years?
7.5
Suppose that we randomly survey one person. Find the probability that person keeps his/her car less than 2.5 years.
0.0122
If we are to pick individuals 10 at a time, find the distribution for the mean car length ownership.
$N\left(\mathrm{7,0}\text{.}\text{63}\right)$
If we are to pick 10 individuals, find the probability that the sum of their ownership time is more than 55 years.
0.9911
For which distribution is the median not equal to the mean?
B
Compare the standard normal distribution to the student-t distribution, centered at 0. Explain which of the following are true and which are false.
The next five questions refer to the following information:
We are interested in the checking account balance of a twenty-year-old college student. We randomly survey 16 twenty-year-old college students. We obtain a sample mean of $640 and a sample standard deviation of $150. Let $X$ = checking account balance of an individual twenty year old college student.
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?
student-t with $\text{df}=\text{15}$
Find the 95% confidence interval for the true mean checking account balance of a twenty-year-old college student.
$\left(\text{560}\text{.}\text{07},\text{719}\text{.}\text{93}\right)$
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