Critical Values and Confidence Intervals

What you’ve been doing…  Gathering Data  Calculating Data  Interpreting Data With surveys, experiments, and simulations, you only sample the population.

With a census, the entire population is used (to the best of the census taker’s ability).

Do you remember?  Population: the entire group  Parameter: an unknown proportion which describes the population (called p)  Sample: a smaller group which will describe the population  Statistic: a value calculated of the sample, generalized to describe the population (called p-hat)

So how can we use this???  If you are given the example: The 2001 Youth Risk Behavioral Survey questioned a nationally representative sample of 12,960 students in grade Of these, 3340 said they had smoked cigarettes at least one day in the past month.  How can you represent the data listed above?

High School Students and Smoking  Population:Students in grades 9-12 in the United States.  Parameter: Proportion of students in grades 9-12 who have smoked cigarettes at least once in the past month.  Sample: 12,960 students randomly selected to represent students in grade 9-12 in the United States  Statistic: 3,340 out of 12,960 students said they have smoked cigarettes at least once in the past month (this is p-hat)…  Which ≈ or 25.77%

So we can say…  In the United States, among high school students, grade 9-12, there are 25.77% of students who say they have smoked cigarettes at least once in the past month.  However, we can add to this statement to make it more accurate…

Since we cannot be that EXACT, we need to give a range or “spread” of data…  In order to do this, we need to use a new formula:  z* is the critical value (coming up)  n is the number of items in the sample.

Remember, the Rule? This is better!

So, now… O p-hat = O 1-p-hat = O n=12960 O And for a 95% confidence interval (the standard), z* is 1.96 O Plug it all in…

The Confidence Statement O We are 95% confident that the true proportion of high school students who have smoked cigarettes at least one day in the past month is between 25.03% and 26.51%.

What’s different???  This statement now includes the margin of error (since nothing’s perfect).

Now, in your groups…  Write a scenario.  Include in your write up the population, parameter, sample, and statistic.  Solve the problem, identifying the value of each variable. Show your work.  Make a generalized statement at the end.