CHAPTER 10a EXERCISES 1. Suppose we perform a valid 1-sided F-test on the populations of male and fe

CHAPTER 10a EXERCISES

1. Suppose we perform a valid
1-sided F-test on the populations of male and female Angus beef cattle. The sample of males has a higher standard
deviation. We correctly compute the
p-value to be 0.068. If we are doing
this F-test at α = 0.05, what is our conclusion?

2. A bolt manufacturer is using
a hypothesis test with α = 0.01 to see if the diameter of
their 0.75 cm diameter bolts are being manufactured properly. The goal is to have the average bolt diameter
be 0.75 ± 0.0075 cms. (Thus, a 2-sided test with difference of 0.0075 is used.)
They know that the standard deviation of the 0.75 cm bolts is 0.028 cms. Use Minitab to compute the sample size
necessary to achieve a power of 0.9.
According to the Power Curve, ifa
difference of 0.0025 must be used, what is the approximate power of the test
using this sample size? Copy and paste
or attach your Minitab output to your paper.

3. In a contentious shareholder
lawsuit, a critical claim by the plaintiffs is that average CEO tenure for companies
of at least $2 billion in market cap is 9 years. A survey of 36 such companies had a sample
mean of 7.90 with a sample standard deviation of 6.45. Use this sample to test at the 5% level
whether the average CEO tenure is less than 9 years. Do the test by hand (using Minitab just for
the p-value) and confirm your results with Minitab. Interpret your results and state your
conclusion in terms of the data.

4. Statistical significance, Power, and Practical
significance – A Big Data Issue: As a
marketing associate for a sports apparel company, we see that, in 2011, 44.2%
of our customers checked reviews of our new products on social media sites
before buying. This year, to see if that
percentage has increased, we use an email campaign to survey our recent
customers. Of 39,994 respondents, 17,885
said that, before buying, they checked reviews of the product they purchased on
social media.
a. Based on this survey, what is
the point estimate of the proportion of our customers who check social media
reviews?
b. Test whether the increase
indicated by this point estimate is statistically significant?
c. Compute a 95% confidence
interval for the percentage of customers using social media before buying. What do we think about it?
d. What is the power of the test
in part b?
e. Based on this analysis, would
you recommend any changes in our social media marketing approach?

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