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Examination 4
Page 1
You are allowed to operate a calculator and refer to one page of notes and the tables from the textbook while taking this examination. Your solutions should be clear, complete, and sufficiently detailed in order to demonstrate your understanding and communicate your reasoning and method of solving the problem. Each problem will be graded on a 5-point standard scale.
Student’s Name
Problem 1
In the most recent Gallup poll, 2206 of the 3559 Americans polled approved of the job Barack Obama is doing as president.
Using a 95% confidence interval, estimate the actual percentage of Americans that presently approve of the job Barack Obama is doing as president. Express your answer symbolically and verbally.
Solution
60.4% < p < 63.6%
With 95% confidence, the actual percentage of Americans that
presently approve of the job Barack Obama is doing as president is
estimated to be between 60.4% and 63.6%.
Examination 4
Page 2
Problem 2
The total annual revenue (in billions of dollars) generated by Google for the previous 6 years is given in the table below.
Year 2003 2004 2005 2006 2007 2008 Revenue 1.5 3.2 6.1 10.6 16.6 21.
(a) Find the regression line that will best predict Google’s total annual revenue for a given year.
(b) How strong is the linear relationship between Google’s total annual revenue and the corresponding year? Use words and statistics to support your answer.
(c) Predict Google’s total annual revenue for 2009. Use words to state your answer.
L 1
L 2
The regression line is y = 4.18 x – 8367.
where y is the total annual revenue (in billions
of dollars) and x is the corresponding year.
Since r = 0.982 is very close to one, there is a very strong linear
relationship between Google’s total annual revenue and the
corresponding year.
Google’s total annual revenue for 2009 is predicted to be about
30.33 billion dollars.
y = 4.18 2009⋅ − 8367.29 =30.
Examination 4
Page 4
Problem 4
The price for a gallon of regular grade gasoline was collected for a random sample of 18 gas stations in the Sacramento area. The results were as follows: $2.23, $2.25, $2.19, $2.28, $2.25, $2.25, $2.23, $2.19, $2.27, $2.23, $2.29, $2.24, $2.20, $2.28, $2.24, $2.23, $2.25, and $2.21.
Is there sufficient sample evidence, at the 0.05 level of significance, to conclude that the mean price for regular gasoline in the Sacramento area is below $2.30 per gallon?
0
1
: $2.
: $2.
H
H
μ
μ
≥
< The mean price for regular gasoline in the
Sacramento area is below $2.30 per gallon.
Let α = 0.
Since the p-value ≈ 0.000 ≤ 0.05 = α, we reject Ho.
Hence, there is sufficient sample evidence, at the 0.05 level of significance,
to conclude that the mean price for regular gasoline in the Sacramento area
is below $2.30 per gallon.
Examination 4
Page 5
Problem 5
A book publisher wishes to determine whether there is a difference in the type of book selected by men and women for recreational reading. A random sample produced the data given below.
Mystery Romance Self-help
Men 243 201 191
Women 135 149 202
Is the type of book selected independent of the gender of the individual? Use α = 5%. Based on this result, what can the book publisher conclude?
Let α = 5%
H 0 : The type of book selected is independent of gender.
H 1 : The type of book selected is not independent of gender.
Since the p-value ≈ 0.0% ≤ 5% = α, we reject Ho.
Hence, the type of book selected is not independent of the gender of the
individual.
So, based on this result, the book publisher can conclude that there is a
difference in the type of book selected by men and women for recreational
reading. Men were more likely to select a mystery; whereas, women were more
likely to select a self-help book.
