In this activity, we will estimate a confidence interval for the proportion of times a Hersheys kiss lands on its base as opposed to its side. To do this, we will drop Hersheys kisses, count how many land on their base, and calculate the confidence interval.

To take your sample, gather five Hersheys kisses in a cup, shake them up, and drop them from about six inches above a desk/table. Count the number that land on their base. Repeat this ten times to get a sample of 50, recording your results in the table below:

Toss Number	Number that land on base
1
2
3
4
5
6
7
8
9
10

Total count (out of 50) =

What is the population of interest?

What is the sample?

Find the proportion of kisses that land on their base in the 50 tosses combined: =

(This is a sample proportion, and sample proportions are denoted by .)

All students in our class are going to be doing this activity. If you were to compare your with theirs, do you think everyone would get the same answer? Why or why not?

Follow these steps to make a 95% confidence interval for the population proportion, p, based on your .

1. Calculate the standard deviation of your sample proportion (this is called the standard error). Use the equation , where n is the sample size and . Show your work:
2. Look up the critical value, z*, that corresponds to 95% confidence. Note, this is the z-score that corresponds to the middle 95% of the normal distribution. (Hint: what percentage would be left in each tail of the distribution? Draw a picture and use the z-score from p-value calculator applet to find the z- score). The positive z-score is the critical value:
3. Find the margin of error for the confidence interval: ME )(
4. Now find the confidence interval. Adding and subtracting the margin of error from the sample statistic creates the lower and upper bounds for the confidence interval: CI )(.

your lower bound = ___________ your upper bound = ____________

Use the lines below to roughly draw your confidence interval (use a textbox). Indicate the location of as a dot. (An example of a CI from 0.13 to 0.37 with = 0.25 is given.)

Interpret the 95% confidence interval in your own words. Write your interpretation here:

If youve completed these tasks and questions, eat a Hersheys Kiss while you ponder the following:

Which of the following do you think is true (more than one may be true)?

1. There is a 95% probability that the true proportion will fall in your interval.
2. There is a 95% probability that your interval will include the true proportion.
3. BEFORE we take the sample, there is a 95% probability that the confidence interval we will create WILL include the true proportion.
4. AFTER we take the sample, there is a 95% probability that the confidence interval we created DOES include the true proportion.