Lindsey D. Bell
Math 1040
Tiffany Hilton
Term Project Part 6- Hypothesis Testing
Part 6: Hypothesis Tests (1% of course grade)
Explain in general the purpose and meaning of a hypothesis test.
Answer: A hypothesis test is the procedure used to test a claim about a property of a population,
meaning: when given a claim about a certain population, we can use the hypothesis test to determine if
the claim is true or not, whether to reject or fail to reject the claim, if there is sufficient or insufficient
evidence relevant to the claim and be able to state the conclusion about the claim in simple and
nontechnical terms.
Red
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Lindsey D. Bell
Math 1040
Tiffany Hilton
Term Project Part 6- Hypothesis Testing
Using values for the class data that you computed in Part 3 of the project and a 0.05 significance level,
test the claim that 20% of all Skittles candies are red. Show all the steps (neatly written and scanned
or typed). Discuss and interpret the results.
Answer: Class Total of Red Skittles = 326
p: proportion of skittles that are red (class population)
H0: p=0.20, H1: p≠0.20
x= 326, n= 27, p= 0.20, p-hat (x/n) = 326/27= 12.074, q (1-n) = 1-0.20= 0.80
z= p-hat-p/sqrt (p*q/n)
z= (326/27)-0.20/ sqrt ((0.20) (0.80)/326) = 3.05
z= 0.9989
p-value = 1-0.9989= 0.0011
*Since 0.0011 <0.05 (significance level) we reject the null hypothesis; we reject the null hypothesis that
0.20 of Skittles candies in a regular sized bag are red candies.
Using values for the class data that you computed in Part 4 of the project and a 0.01 significance level,
test the claim that the mean number of candies in a bag of Skittles more than 55. Show all the steps
H0: p> 55
H1: p< 55
n= 27, x-bar = 12.07407407, n= 27, s= 3.40729902, df= 26
t= x-bar – mu x-bar/s/sqrt n
t= 12.07407407-55/3.40729902/sqrt (27) = -65.462
t=2.479
Lindsey D. Bell
Math 1040
Tiffany Hilton
Term Project Part 6- Hypothesis Testing
List the requirements for doing each of the two hypothesis tests you performed (see pages 400 and 412
in the textbook). Discuss whether or not your samples met each of these requirements. Hint: use the
sampling method from Part 2 of the project to answer part of this. (15 points)
Answer:
Testing a claim about a population proportion
Requirements:
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The sample observations are simple random sample
The conditions for a binomial distribution are satisfied. (There are a fixed number of independent
trials having constant probabilities, and each trial has two outcome categories of “success” and
“failure.”)
The conditions np > 5 and nq > 5 are both satisfied, so the binomial distribution of sample
proportions can be approximated by a normal distribution with mu = np and population standard
deviation = sqrt (n*p*q).
Testing a claim about a population mean (with population standard deviation not known)
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The sample is a simple random sample
Either or both of these conditions is satisfied: the population is normally distributed or n > 30