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Final Review. More Problems.
STAT 145
Problem 1. (formulation is different from Problem 1 (Spring 2013 Exam 4), be careful !)
A tobacco company claims that its best-selling cigarettes contain 40 mg of nicotine. The average nicotine
content from a simple random sample 15 cigarettes is 37.4 mg with a standard deviation (s) of 3.7 mg. Is this
evidence the nicotine content of the cigarettes is less than 40 mg? Assume cigarette nicotine content is
distributed normally. Use a 5% level of significance (α=0.05) to carry out the appropriate test of significance.
Do a) – e) as in Spring 2013 Exam 4 (Final).
Problem 2. (pay attention !)
You want to study the effect instituting a mandatory ergonomics training program. You examine a random
sample of people and observe the number of worker injuries reported before and after their training and their
differences (before minus after taking the training program) are: 1, 2, 3, 4, 1, 0.
* Usually we want the differences be positive in the majority (in this case, before minus after).
Specify the appropriate test of significance and state the hypotheses for the test to determine if there is evidence
that the workers’ number of injuries has decreased after taking the training program?
Just in purpose of visualization, the original data is:
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Final Review. More Problems.
STAT 145
Problem 3. (discussed during Lecture for Chapter 20)
In the 2010 US midterm elections 41% of registered voters actually voted. In the recent 2014 midterm election,
an SRS of 2500 US registered voters found that 915 registered voters actually voted. At the 1% level of
significance, is this evidence the proportion of registered voters who voted in the 2014 midterm election was
less than the proportion who voted in the 2010 midterm election?
a) What is the alternative hypothesis for the appropriate test of significance?
b) Calculate the test statistic.
c) Calculate the p-value.
d) What is the conclusion?
e) To check the conditions for inference for this test of significance, we check for an SRS from the population as
well as … (continue sentence).
NEW, changed
In the 2010 US midterm elections 41% of registered voters actually voted. In the recent 2014 midterm election,
an SRS of 2500 US registered voters found that 1075 registered voters actually voted. At the 1% level of
significance, is this evidence the proportion of registered voters who voted in the 2014 midterm election was
greater than the proportion who voted in the 2010 midterm election?
Do all steps as in the previous problem!!!
Problem 4.
Eggs that are contaminated with salmonella can cause food poisoning among consumers. A large egg producer
takes an SRS of 200 eggs from the eggs shipped in one day. The laboratory reports that 11 of these eggs had
salmonella contamination. Unknown to the producer, 0.2% of all eggs shipped had salmonella. In this situation
a. both 0.2% and 11 are statistics.
b. both 0.2% and 11 are parameters.
c. 0.2% is a parameter and 11 is a statistic.
d. 11 is a parameter and 0.2% is a statistic.
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Final Review. More Problems.
STAT 145
Problem 5.
Select the word(s) from the following alphabetized list that best completes the sentences below, and write the
word(s) in the blank space provided.
Word List: categorical variable, quantitative variable, correlation, distribution, p-value, inference, margin of
error, probability, regression, explanatory variable, response variable, standard error, simple random sample
(SRS), variability, law of large numbers, central limit theorem, parameter, statistic, observational study,
experiment, double-blind experiment, treatment.
(a) The _________________ of any outcome of a random phenomenon is the proportion of times the outcome
would occur in a very long series of repetitions.
(b) The probability, assuming that the null hypothesis is true, that the test statistic would take a value as extreme
or more extreme than that actually observed is called the _____________ of the test.
(c) Statistical __________________ provides methods for drawing conclusions about a population from sample
data.
(d) A ____________________ of size n consists of n individuals from the population chosen is such a way that
every set of n individuals has an equal chance to be the sample actually selected.
(e) A ________________ line is a straight line that describes how a response variable y changes as an
explanatory variable x changes.
(f) The __________________ of a variable tells us what values the variable takes and how often it takes these
values.
(g) When the standard deviation of a statistic is estimated from data, the result is called the
________________________ of the statistic.
(h) The _________________ measures the direction and strength of the linear relationship between two
quantitative variables.
Problem 6.
Doctor examined whether taking aspirin helps with the recovery from heart attacks. The subjects were the 539
patients who were admitted with heart attack or stroke symptoms to a University Hospital in Barcelona, Spain,
between October 1991 and March 1993. The patients were asked by the doctor if they had taken aspirin during
the prior week: 214 said yes and 325 said no. It was found that the group who had taken aspirin had a much
lower amount of permanent damage from their heart attacks than the group who had not taken aspirin. Is this an
observational study or an experiment? Explain your answer.
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Final Review. More Problems.
STAT 145
Problem 7.
In a recent article it was reported that in a random sample of children in grades two through four, a significant
negative relationship was found between the amount of homework assigned and student attitudes.
This is an example of
a. an experiment.
b. an observational study.
c. the establishing of a causal relationship through correlation.
d. a block design, with grades as blocks.
The attitude of the students is
a. an explanatory variable.
b. a response variable.
c. a confounding variable.
d. none of the above.
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