Students On Diets

Here is problem involving sample proportions. This one is about dieting.

Make sure when you are doing these problems that you draw the curves that go with the information. It is much easier to understand what you are doing if you draw the curves and areas.

In all the problems using the sampling distribution you want to compute areas in some original distribution (the -distribution in this case) and you do that by changing things into z-scores and computing the areas under a standard normal curve instead:

The is the population proportion and it corresponds to z = 0

The is the sample proportion and it corresponds to a value in the left graph above. You change it into a z-value in the right graph above by using the formula for the z-score:

where the stddev is given in this case by:

Problem adapted from Moore’s Basic Practice of Statistics

Having a Girl

This is another confidence interval problem involving estimating the percentage of adults who would prefer to have a girl if they could have only one child.

Notice in this one how it is pretty much impossible to even consider polling the entire population, which is all US adults. Looks like not many people would choose to have a girl if they could choose what their only child was!

Computing confidence intervals is pretty straightforward. Just get the E and subtract it from the sample proportion to get the left endpoint of the confidence interval. Then add it to to get the right endpoint of the confidence interval :

Then the confidence level tells us how likely we feel it is the population proportion is in this interval.

Problem adapted from Larson/Farber’s Elementary Statistics

 

Addicted to Smoking

This is a confidence interval problem.

Notice that in this example we computed the z* ourselves based on the 90% confidence level, but for most of the standard confidence levels (90%, 95%, 99%) you should just look them up in the table in our book on page 399.

For 90% confidence level, z*=1.645

For 95% confidence level, z*=1.960

For 99% confidence level, z*=2.576

This one has the memorable quote “If it says confidence interval you know it’s going to be a confidence interval problem.” Yeah!

Problem adapted from Larson/Farber’s Elementary Statistics