NOTE: All requested Minitab output must be copied into your paper.

1. Buy here:
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HOMEWORK 4
NOTE: All requested Minitab output must be copied into your paper.
1. A farmer is considering a new variety of wheat. Heʼll plant it if it has higher
yield. He conducts an experiment with the null hypothesis that the new variety has the
same yield as his old variety, and the alternative hypothesis that the new variety has
higher yield. Heʼll plant the new variety if the null is rejected; otherwise, heʼll keep
planting the old.
a. A Type I error has what consequences?
b. A Type II error has what consequences?
2. A Human Resources officer is directing a hypothesis test to determine if her
company’s hiring practices are resulting in disparate impact (that is, unintentional)
employment discrimination. The null hypothesis for the test is that there is no
disparate impact discrimination. The alternative hypothesis is that there is.
Considering the relative consequences of Type I and Type II errors, should the

2. significance level (α) be set relatively low (around 0.01) or relatively high (around
0.10)? Explain your answer.
3. In many farming areas throughout the Midwest, it can be lucrative for landowners
to have giant wind turbines for the production of electricity constructed on their land.
It is widely accepted that, to be profitable, the average wind speed at the proposed
turbine site should be 8 mph or more. For a site north of West Lafayette, the wind
speed was monitored every 8 hours for a one year period. A total of 1095 readings
had an average speed of 8.305 mph with a standard deviation of 3.909. Considering
the consequences of Type I and Type II error, should we use a relatively high α level
(0.10) or relatively low (0.01) for an appropriate 1-sided hypothesis test using this
data? Explain your answer.
4. A bolt manufacturer is using a hypothesis test with α = 0.05 to see if their 0.85 cm
diameter bolts are being manufactured properly. The goal is to have the average bolt
diameter be 0.85 ± 0.02 cms. Based on past experience, they take the population
standard deviation of the 0.85 cm bolts to be 0.05 cms. They wish to have a power of
0.92.
a. Using Minitab, follow the instructions below to compute the sample size
necessary to attain this power for this test.
5. In random sample of 105 shoppers at the Lafayette Best Buy taken over a one
week period, 56 said they were there “showrooming;” that is, using the Best Buy to
check out products that they intended to buy online. We are interested in whether, at
the 10% level, 50% of Lafayette Best Buy shoppers are showroomers? a. Using the
normal approximation to the binomial, conduct the test by hand. Show all steps in

3. your work, including your hypothesis test set-up and how you determined your
p-value.
b. Next, confirm your results using Minitab. Copy your Minitab output to your
paper.
c. Interpret your hypothesis test conclusion in the context of the data and the
question being studied.
(Stat -> Power and Sample Size -> 1 sample t -> Sample sizes: Leave Blank since this
is what we are computing; Differences: 0.02 ; Power values: 0.92 ; -> Standard
Deviation: 0.05 ->Options:Alternative Hypothesis: ≠ ; Significance Level: 0.05)
b. Suppose they decide that the test should be conducted α = 0.01. All other
inputs being equal, will the necessary sample size be greater, less than, or equal to
that computed in part a. Explain your answer. (Hint: You can use Minitab to actually
get the answer.)
6. In a random sample of 38 large cap mutual funds, the average 2016 return is
2.16% with a standard deviation of 9.08%. a. Use Minitab to test at the 5% level
whether the average 2016 return for a large cap mutual fund is positive.
b. State your test conclusion in the context of the data and the question being
studied.
c. Using Minitab, create a graph showing that the test statistic reported by Minitab
gives the test p-value.

4. 7. A company is deciding whether to renew its ad buy with a local TV station. It will
renew the ad if a 2-sided hypothesis test at the 10% level using the normal
approximation method concludes that more than 17% of the local residents remember
the ad. They decide to test this by contacting 525 randomly selected local residents.
One-hundred-and-one (101) of the 525 remember the ad. a. Conduct the requested
hypothesis test based on this sample using the normal approximation method. (Use
Minitab.) Report your conclusions, stated in the context of the data and the question
being studied.
b. Using Minitab, create a graph showing that the test statistic reported by
Minitab gives the test p-value.
c. The station advocates that the decision be made based on a 1-sided
hypothesis test at the 10% level using this sample. Why? (Hint: If you conduct the
appropriate 1-sided test using the normal approximation based on this sample, what
will the p-value be? You can confirm your answer with Minitab by conducting this
1-sided test.)
8. As Quality Control officer for the Maui Onion Potato Chips division of the Tasty
Hawaiian Snacks Co., we decide to test whether our chip bagger is correctly bagging
our 28.3 gram snack bags. We randomly sample 58 bags from the production line.
The weights of the bags (gms) are recorded in the MauiOnionChips dataset. a.
Use Minitab to conduct a 2-sided hypothesis test at the 10% level based on our
sample. Report your conclusion, stated in the context of the data and the question
being studied.
b. Use Minitab to compute a 5-number summary and to draw a boxplot of this
data. Based on these, what issues do we see with our hypothesis test?

5. 9. Open the WoolBreaks dataset and use Minitab to test at the 10% level whether
there is a difference in average thread breaks between Wool A and Wool B. (Note that
since both sample sizes are less than 30, we must assume that thread breaks are
normally distributed in order for the test to be valid.)
a. Assume the test is valid and interpret the results in the context of the data and
the question being studied.
b. Using Minitab, create a graph showing that the test statistic given by Minitab
produces the test p-value.
c. Considering what we have seen when working with this data, explain why this
test result is misleading.
10. A consumer products researcher randomly surveyed 900 people and asked them
if they try to avoid eating fast food. Of the 455 respondents who were 34 or younger,
229 said they did. Of the 445 who were 35 or older, 284 said they did.
a. Using Minitab, test at the 5% level for a difference in fast food avoidance between
these two age groups and interpret the test results in the context of the data.
b. Using Minitab, create a graph showing that the test statistic given by Minitab
produces the test p-value.