BreAnn McKee
Introduction to Statistics 1040
Justin Christensen, T/Th 5:30-6:50pm
Skittles Term Project: Confidence interval estimate and Hypothesis tests.
 The general propose and meaning of a Confidence Interval.
A confidence Interval is a range of values used to estimate the true value of a population
parameter, instead of a single value. A confidence interval gives us a much better sense of how
good an estimate is, and is associated with a confidence level of success rate of the procedure. A
confidence interval can be used to test a claim made about a population proportion, and can
help make an informal judgment based on the result.
 Construct a 99% confidence interval estimate for the true proportion of yellow
candies.

Results
Sample Size: 289
Observed Proportion: 20%
Confidence Level: 99%
Confidence Interval: ±6.06
Range for the true population proportion of yellow candies.
= 13.94% to 26.06%, percent of yellow candies, a proportion estimate in a bag of
Skittles.
 Construct a 95% confidence interval estimate for the true mean number of candies per
bag.
 Results
Sample size =24 bags of candies
Mean= 60.9
Standard deviation= 2.01
Confidence interval of ±0.8
Range for the true population mean = 60.1 – 61.7 for the mean number of candies per
bag of Skittles

Construct a 98% confidence interval estimate for the standard deviation of the
number of candies per bag.

Results

1.537< Ҩ <2.1294, = range mean standard deviation for the number of candies per bag.
With a 98% Confidence interval level, the repeated experiment for the proportion of candies per
bag, skittles would have a confidence interval estimate for the standard deviation such as
intervals contain the estimated population mean would be 98%.
:
 Discussion and interpretation of my results from the three confidence interval estimates.
The results from my three confidence interval estimates are a true value of proportion of the
population for Skittles. The ranges of the width of skittles may vary from the samples I have
collected. If I had a larger sample size the confidence intervals would be a larger range for the
sample size. But my findings have shown that with high confidence levels that the ranges I got
are the best estimate for the true values of Skittles.
Confidence Interval:
±0.8ange
for the population mean:
60.
 The general meaning and purpose of a Hypothesis Tests
In statistics a hypothesis is a claim or statement about a property of a population. A hypothesis
test is a procedure for testing a claim about a property of a population. The use of the word
property correlates with the definition of a population parameter. Using the hypothesis test we
can answer questions with the most effective outcome to a conclusion or a claim that is made.
 Use a 0.05 significance level to test the claim the 20% of all Skittle candies are Red.
 Results
.05 significance level of a claim that 20% of all skittles are Red:
T score = -1154.297
P-value = 0
Since the P-value is < then the significance level of .05, we can reject the null
hypothesis.
µ= 60.9 X= 320 S= 2.01 Ṕ=1461 Sig. level = .05
T- value = 4927.15771, P-value = 2
P-value is > the significance level .05, we cannot reject the null hypothesis.
 Use a 0.01 significance level to test the claim that the mean number of candies in a
bag of Skittles is 55.
 Results
X= 24 µ=60.9 Ҩ=2.01 p=55 Significance level .01
T-score = -136.14812 P-value = 0
P-value is 0 < the sig. level of .01, we can reject the null hypothesis
 Discussion and interpretation of the two hypothesis tests.
The hypothesis is procedure to test the claim made about a value proportions, from my findings
above I have discovered that the claim of more red Skittles is true and the average candies per
bag is not 55. Samples sizes vary so much that the only way to get a broad scope on the average
amount of candies per bag, is to survey a larger population on the amount of skittles per bag.
Then the ranges could be much higher then my findings and a larger mean of candies per bag
could be found.
 Reflection
The conditions and terms for Confidence Intervals and Hypothesis Tests are gathering a sample
size for a claim you would like to verify. With Skittles the idea is to verify that there are is a
specific amount of each color of skittles per bag. The original data collected showed me that this
is always a deviation in amount per bag and amount of color. To get a smaller rage of deviation
we would need to survey the entire student bodies through put SLCC. Then we could get a
better idea of the true amount and a better claim per bag of candy.
There could be several errors made with the calculations for both tests, because of the use of
several different formulas and the rounding off of final counts. Improvements for these types of
problems would be to reduce the amount of formulas need to find ranges or even T-scores, pvalues, and z-scores. There should be an all in one formula and a table to show the additional
information we might need for the claims.
My conclusion to this type of research is the more accurate of findings would be a larger
population needed to survey and a less invasive calculation to find claims. This would be the
best way to get a true idea of a population portion for even the simple things in life, like a bag of
Skittles.