1) label the Hypothesis Testing Model with the Critical values and Test Statistics
2) list any calculator function(s) you use with the appropriate values you used to answer the
question. 3) round z scores & percentages to 2 decimal places and decimal probabilities to 4
decimal places.
1. A food manufacturer claims that their new low-fat oat
an muffin has a population mean fat
content of 5 grams with a population standard deviation of 0.89 grams. A government food researcher
elieves the manufacturer's claim is too low and decides to test the manufacturer's claim. A random
sample of 35 muffins yields a sample mean fat content of 5.3 grams. The food researcher decides to
perform a hypothesis test at
α = 5 % to determine if it is reasonable to reject the manufacturer’s claim. ​I. ​State the hypotheses (in
words & symbols):
H0:_______________________________________________________________
Ha:_______________________________________________________________
II. ​Determine the model to test H0
a) Can you use a normal distribution for the Sampling Distribution model to perform this test? Please
explain. If not, then what distribution could you use?
_________________________________________________________________
2b) Using the appropriate notation, state the MEAN & STD ERROR of the sampling distribution:
Mean:____________________________________________________________
STDE
or:__________________________________________________________
III. ​Determine the Decision Rule​:
State the decision rule:
____________________________________________________________
IV. Analyze the sample data: Using the appropriate notation, state the sample result of the test,
p-value and the test statistic.
sample result is:____________________________________________________
p-value is: ______________________________________________________
test statistic is: _____________________________________________________
V. State the Conclusion: ___________________________________________________
Answer Question: Do you believe that it is reasonable to agree with the researcher's claim at α = 5%?
YOU MUST EXPLAIN YOUR ANSWER OTHERWISE: No credit will be given.
_________________________________________________________________
2. An FM rock station claims that 85% of all its listeners are college students. A statistician decides to
test this claim against the suspicion that the percentage is too high.
A random sample of 2000 listeners is selected from the population of all listeners and it is determined
that 1655 are college students. Perform a hypothesis test to answer the question: Do the sample
esults support the statistician’s claim at α = 1 %?
I. State the hypotheses (in words & symbols):
H0:_______________________________________________________________
Ha:_______________________________________________________________
II. ​Determine the model to test H0
Can one use a normal distribution for the Sampling Distribution model to perform this test? Please
explain. _________________________________________________________________
) Using the appropriate notation, state the MEAN & STD ERROR of the sampling distribution:
Mean:____________________________________________________________
STDE
or:__________________________________________________________
III. Determine the Decision Rule:
State the decision rule: ________________________________________________________
IV. Analyze the sample data: Using the appropriate notation, state the sample result of the test,
p-value and the test statistic.
sample result is:____________________________________________________
p-value is: _________________________________________________________
test statistic is: _____________________________________________________
V. State the Conclusion: ___________________________________________________
Can the statistician reject the rock station's claim at α = 1%? YOU MUST EXPLAIN YOUR ANSWER
OTHERWISE: No credit will be given.
_________________________________________________________________
3) A random sample of 900 M&Ms is selected from the population of plain M&Ms where the
population proportion of red M&Ms is 35%.
a) State the mean and standard e
or of the sampling distribution using the proper notation for the
mean and standard e
or.
_________________________________________________________________
) Can the sampling distribution be approximated by a normal distribution? Show work to support
your answer.
_________________________________________________________________
c) Using the sampling distribution, calculate the probability that a sample of 900 M&Ms selected at
andom contains at least 37% red M&Ms. Draw graph and shade area representing the probability on
the graph. Show work!! Show the calculator functions with input data that you used to solve this
problem.
4) You are hired by a cell phone provider to determine the number of times per day their customers
interact with their smartphone. You take a random sample of 25 customers and find the average
number of interactions to be 75 times per day with a sample standard deviation of 5.
4 a. If you decide to construct a confidence interval for the population mean number of interactions,
what distribution would you use and why?
. Construct a 99% confidence interval estimate for the population mean number of interactions.
c. What is the margin of e
or for the confidence interval you found in part b?
d. A representative for the cell phone provider told you they believe the mean number of interactions
per day was 83. What would you say to the company representative? Explain.
5) A statistics student at a New York State community college, randomly samples 500 students who
own cell phones to determine if they play games on their phones. 65% stated that they use their
mobile phones to play games.
Using this information, then:
a) construct a 95% confidence interval (to 3 decimal places) for the population proportion, p, of NYS
community college cell phone users who play games on their phones.
) construct a 99% confidence interval for the population proportion, p, of NYS community college cell
phone users who play games on their phones.
c) determine the margin of e
or for both the 99% and 95% confidence interval estimates.
d) What did you notice about the relationship between the confidence interval width and the margin
of e
or as the confidence interval increased from 95% to 99%?
e) Would it be reasonable for someone to state that 75% of NYS community college cell phone users
play games on their cell phones? ​YOU MUST EXPLAIN YOUR ANSWER OTHERWISE: No
credit will be given.
6) The name of theorem that states:
For any population, regardless of the shape of the population being randomly sampled, the sampling
distribution of the mean can be reasonably approximated by a normal distribution whenever the
sample size n is greater than 30.
The theorem:
7) The Speedy Oil Change Company advertises that the average mean time it takes to change a
customer's oil is 10 minutes. After receiving complaints from dissatisfied customers, the management
at Speedy Oil Change headquarters hired a researcher to investigate the complaints to determine if
the oil change took significantly longer than 10 minutes. The researcher randomly investigates 20 oil
changing jobs and computes the sample mean time to change a customer’s oil is 11.3 minutes with a
sample standard deviation of 3.3 minutes. Based on this sample result, the researcher decides to
conduct a hypothesis test to determine if Speed Oil Change Company’s claim is statistically too low at
α = 5 %?
I. ​State the hypotheses ​(in words & symbols):
H0:_______________________________________________________________
Ha:_______________________________________________________________
II.​ ​Determine the model to test H0
a) Can you use a normal distribution for the Sampling Distribution model to perform this test? Please
explain. If not, then what distribution could you use?
) Using the appropriate notation, state the MEAN & STD ERROR of the sampling distribution:
Mean:____________________________________________________________
STDE
or:__________________________________________________________
III.​ Determine the Decision Rule:
State the decision rule: ____________________________________________________________
IV. Analyze the sample data: Using the appropriate notation, state the sample result of the test,
p-value and the test statistic.
sample result is:____________________________________________________
p-value is: ______________________________________________________
test statistic is: _____________________________________________________
V. State the Conclusion: ___________________________________________________
Answer Question: Based on this sample result, can the researcher conclude that Speed Oil Change
Company’s claim is too low at α = 5 %? YOU MUST EXPLAIN YOUR ANSWER OTHERWISE: No credit
will be given.