1 | GB 513 Unit 3 Success Guide v.6.13.17
UNIT 3 SUCCESS GUIDE
This unit is the other “most difficult” one. Hypothesis testing has two parts: setting-up the hypotheses and calculating the critical values to determine results. They both pose difficulty for a lot of students. The seminar will be on the first and the recorded lecture will be on the second. You need to make sure you understand both, otherwise you will not be able to get to the right conclusions.
1. As always, start by reading the chapters and studying the solved examples.
2. Watch the lecture video in document sharing. It focuses on why we do
hypothesis testing, how to do it with Excel and solves two sample problems.
3. Watch this from Khan Academy:
This one talks more about how to write the null and alternative hypotheses
(which a lot of students get wrong) and also solves the problem using
4. Watch the sample problem solutions in Course Resources.
5. If you still want more videos, search YouTube for “hypothesis testing.” Several
introductory level videos are available, such as
Email your instructor if you find any of these links to be broken.
Avoid these mistakes!
COMMON MISTAKES IN THE ASSIGNMENT
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Students commonly get the null and alternative hypotheses reversed, or
get them completely wrong.
Students also commonly do not state the hypothesis fully. This is correct:
“null hypothesis: there is no difference between the average salary for
group 1 and the average salary of group 2.” This is not sufficient: “ho:
Students sometimes compare the averages of the two groups and base
their determination on which one is greater, rather than properly doing a
Students sometimes do the calculations correctly, but do not write out
what the conclusion is. This is correct: “We therefore reject the null
hypothesis, which means we conclude that there is a difference between
the average salaries of the two groups.” This is not sufficient: “reject null.”
In the last problem, students run the test but then have no idea which
metric to use in order to make a conclusion.
The questions below are very similar to what you need to solve in the assignment.
Some, but not all, of these solutions were demonstrated on video and recorded
for the live binder by the math tutors.
SAMPLE PROBLEM 1 FOR ASSIGNMENT PROBLEM 4
A hole-punch machine is set to punch a hole 1.84 centimeters in diameter in a
strip of sheet metal in a manufacturing process. The strip of metal is then creased
and sent on to the next phase of production, where a metal rod is slipped
through the hole. It is important that the hole be punched to the specified
diameter of 1.84 cm. To test punching accuracy, technicians have randomly
sampled 12 punched holes and measured the diameters. The data (in
centimeters) follow. Use an alpha of .10 to determine whether the holes are being
punched an average of 1.84 centimeters.
Assume the punched holes are normally distributed in the population.
1.81 1.89 1.86 1.83 1.85 1.82 1.87 1.85
1.84 1.86 1.88 1.85
SAMPLE PROBLEMS AND SOLUTIONS
n = 12 x = 1.85083 s = .02353 df = 12 – 1 = 11 = .10
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SAMPLE PROBLEM 2 FOR ASSIGNMENT PROBLEM 4
The following data (in pounds), which were selected randomly from a normally
distributed population of values, represent measurements of a machine part that
is supposed to weigh, on average, 8.3 pounds.
8.1 8.4 8.3 8.2 8.5 8.6 8.4 8.3 8.4 8.2
8.8 8.2 8.2 8.3 8.1 8.3 8.4 8.5 8.5 8.7
Use these data and alpha =0.01 to test the hypothesis that the parts average 8.3
SAMPLE PROBLEM 1 FOR ASSIGNMENT PROBLEM 5
H0: µ = 1.84
Ha: µ 1.84
For a two-tailed test, /2 = .05 critical t.05,11 = 1.796
t = = 1.59
Since t = 1.59 < t11,.05 = 1.796,
The decision is to fail to reject the null hypothesis
n = 20 x = 8.37
Ho: µ = 8.3
s = .1895 df = 20-1 = 19 = .01
Ha: µ 8.3
For two-tail test, /2 = .005 critical t.005,19 = ±2.861
t = = 1.65
Observed t = 1.65 < t.005,19 = 2.861
The decision is to Fail to reject the null hypothesis
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The Independent Insurance Agents of America conducted a survey of insurance
consumers and discovered that 48% of them always reread their insurance
policies, 29% sometimes do, 16% rarely do, and 7% never do. Suppose a large
insurance company invests considerable time and money in rewriting policies so
that they will be more attractive and easy to read and understand. After using
the new policies for a year, company managers want to determine whether
rewriting the policies significantly changed the proportion of policyholders who
always reread their insurance policy. They contact 380 of the company’s
insurance consumers who purchased a policy in the past year and ask them
whether they always reread their insurance policies. One hundred and sixty-four
respond that they do. Use a 1% level of significance to test the hypothesis.
SAMPLE PROBLEM 2 FOR ASSIGNMENT PROBLEM 5
A survey was undertaken by Bruskin/Goldring Research for Quicken to determine
how people plan to meet their financial goals in the next year. Respondents were
allowed to select more than one way to meet their goals. Thirty-one percent said
that they were using a financial planner to help them meet their goals. Twenty-
four percent were using family/friends to help them meet their financial goals
followed by broker/accountant (19%), computer software (17%), and books
(14%). Suppose another researcher takes a similar survey of 600 people to test
these results. If 200 people respond that they are going to use a financial planner
to help them meet their goals, is this proportion enough evidence to reject the
31% figure generated in the Bruskin/Goldring survey using
If 158 respond that they are going to use family/friends to help them meet their
financial goals, is this result enough evidence to declare that the proportion is
significantly higher than Bruskin/Goldring’s figure of .24 if alpha = 0.05?
Ho: p = .48
Ha: p .48
n = 380 x = 164 = .01 /2 = .005 z.005 = +2.575
z = = -1.89
Since the observed z = -1.89 is greater than z.005= -2.575, the decision is to
fail to reject the null hypothesis. There is not enough evidence to declare that
the proportion is any different than .48.
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SAMPLE PROBLEM FOR ASSIGNMENT PROBLEM 6
Since the Assignment requires you to use the data analysis tool pack for this
problem, the best way to prepare is to watch the lecture video, which gives two
examples, both solved using Excel.
Ho: p = .31
Ha: p .31
n = 600 x = 200 = .10 /2 = .05 z.005 = +1.645
z = = 1.23
Since the observed z = 1.23 is less than z.005= 1.645, the decision is to fail to reject
the null hypothesis. There is not enough evidence to declare that the proportion
is any different than .31.
Ho: p = .24
Ha: p > .24
n = 600 x = 158 = .05 z.05 = 1.645
Since the observed z = 1.34 is less than z.05= 1.645, the decision is to fail to reject
the null hypothesis. There is not enough evidence to declare that the
proportion is less than .24.
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Khan, S. (2017). Hypothesis testing and p-values. Retrieved from
Perdiscotv. (2010, January 14). Introductory statistics – Chapter 8: Hypothesis testing.
Retrieved from https://www.youtube.com/watch?v=HmMjS88eSVE
Statistics learning centre. (2011, December 5). Hypothesis tests, p-value – Statistics help.
Retrieved from https://www.youtube.com/watch?v=0zZYBALbZgg