Chapter 24 Assignments
2
6
14
16
20
24
26
Chapter 24 #2
2. Stereograms appear to be composed entirely of random dots. However, they contain separate
images that a viewer can “fuse” into a three-dimensional (3D) image by staring at the dots while
defocusing the eyes. An experiment was performed to determine whether knowledge of the
form of the embedded image affected the time required for subjects to fuse the images. One
group of subjects (group NV) received no information or just verbal information about the shape
of the embedded object. A second group (group VV) received both verbal information and visual
information (specifically, a drawing of the object). The experimenters measured how many
seconds it took for the subject to report that he or she saw the 3D image. [To try a few
stereograms see http://klauanna.blogspot.com/2011/10/stereogram.html ]
2-Sample t-interval for 𝝁𝟏−𝝁𝟐
Conf level = 90%
df = 70
𝝁ࡺࢂ −𝝁ࢂࢂ interval: (0.55, 5.47)
Chapter 24 #2
2. Stereograms appear to be composed entirely of random dots. However, they contain separate images that a
viewer can “fuse” into a three-dimensional (3D) image by staring at the dots while defocusing the eyes. An
experiment was performed to determine whether knowledge of the form of the embedded image affected the time
required for subjects to fuse the images. One group of subjects (group NV) received no information or just verbal
information about the shape of the embedded object. A second group (group VV) received both verbal information
and visual information (specifically, a drawing of the object). The experimenters measured how many seconds it
took for the subject to report that he or she saw the 3D image. [To try a few stereograms see
http://klauanna.blogspot.com/2011/10/stereogram.html ]
2-Sample t-interval for 𝝁𝟏−𝝁𝟐
Conf level = 90%
df = 70
𝝁ࡺࢂ −𝝁ࢂࢂ interval: (0.55, 5.47)
a) Interpret your interval in context.
Chapter 24 #2
2. Stereograms appear to be composed entirely of random dots. However, they contain separate images that a
viewer can “fuse” into a three-dimensional (3D) image by staring at the dots while defocusing the eyes. An
experiment was performed to determine whether knowledge of the form of the embedded image affected the time
required for subjects to fuse the images. One group of subjects (group NV) received no information or just verbal
information about the shape of the embedded object. A second group (group VV) received both verbal information
and visual information (specifically, a drawing of the object). The experimenters measured how many seconds it
took for the subject to report that he or she saw the 3D image. [To try a few stereograms see
http://klauanna.blogspot.com/2011/10/stereogram.html ]
2-Sample t-interval for 𝝁𝟏−𝝁𝟐
Conf level = 90%
df = 70
𝝁ࡺࢂ −𝝁ࢂࢂ interval: (0.55, 5.47)
b) Does it appear that viewing a picture of
the image helps people “see” the 3D image
in a stereogram?
Chapter 24 #2
2. Stereograms appear to be composed entirely of random dots. However, they contain separate images that a
viewer can “fuse” into a three-dimensional (3D) image by staring at the dots while defocusing the eyes. An
experiment was performed to determine whether knowledge of the form of the embedded image affected the time
required for subjects to fuse the images. One group of subjects (group NV) received no information or just verbal
information about the shape of the embedded object. A second group (group VV) received both verbal information
and visual information (specifically, a drawing of the object). The experimenters measured how many seconds it
took for the subject to report that he or she saw the 3D image. [To try a few stereograms see
http://klauanna.blogspot.com/2011/10/stereogram.html ]
2-Sample t-interval for 𝝁𝟏−𝝁𝟐
Conf level = 90%
df = 70
𝝁ࡺࢂ −𝝁ࢂࢂ interval: (0.55, 5.47)
c) What’s the margin of error for this
interval? (Show any work.)
Chapter 24 #2
2. Stereograms appear to be composed entirely of random dots. However, they contain separate images that a
viewer can “fuse” into a three-dimensional (3D) image by staring at the dots while defocusing the eyes. An
experiment was performed to determine whether knowledge of the form of the embedded image affected the time
required for subjects to fuse the images. One group of subjects (group NV) received no information or just verbal
information about the shape of the embedded object. A second group (group VV) received both verbal information
and visual information (specifically, a drawing of the object). The experimenters measured how many seconds it
took for the subject to report that he or she saw the 3D image. [To try a few stereograms see
http://klauanna.blogspot.com/2011/10/stereogram.html ]
2-Sample t-interval for 𝝁𝟏−𝝁𝟐
Conf level = 90%
df = 70
𝝁ࡺࢂ −𝝁ࢂࢂ interval: (0.55, 5.47)
d) Explain carefully what the 90% confidence
level means.
Chapter 24 #2
2. Stereograms appear to be composed entirely of random dots. However, they contain separate images that a
viewer can “fuse” into a three-dimensional (3D) image by staring at the dots while defocusing the eyes. An
experiment was performed to determine whether knowledge of the form of the embedded image affected the time
required for subjects to fuse the images. One group of subjects (group NV) received no information or just verbal
information about the shape of the embedded object. A second group (group VV) received both verbal information
and visual information (specifically, a drawing of the object). The experimenters measured how many seconds it
took for the subject to report that he or she saw the 3D image. [To try a few stereograms see
http://klauanna.blogspot.com/2011/10/stereogram.html ]
2-Sample t-interval for 𝝁𝟏−𝝁𝟐
Conf level = 90%
df = 70
𝝁ࡺࢂ −𝝁ࢂࢂ interval: (0.55, 5.47)
e) Would you expect a 99% confidence
level to be wider or narrower? Explain.
Chapter 24 #2
2. Stereograms appear to be composed entirely of random dots. However, they contain separate images that a
viewer can “fuse” into a three-dimensional (3D) image by staring at the dots while defocusing the eyes. An
experiment was performed to determine whether knowledge of the form of the embedded image affected the time
required for subjects to fuse the images. One group of subjects (group NV) received no information or just verbal
information about the shape of the embedded object. A second group (group VV) received both verbal information
and visual information (specifically, a drawing of the object). The experimenters measured how many seconds it
took for the subject to report that he or she saw the 3D image. [To try a few stereograms see
http://klauanna.blogspot.com/2011/10/stereogram.html ]
2-Sample t-interval for 𝝁𝟏−𝝁𝟐
Conf level = 90%
df = 70
𝝁ࡺࢂ −𝝁ࢂࢂ interval: (0.55, 5.47)
f) Might that change your conclusion in
part b? Explain.
Chapter 24 #6
Chapter 24 #6
a) What do the boxplots suggest about any gender differences in pulse rates? (Comment on
location of median and spread of each boxplot.)
Chapter 24 #6
b) Is it appropriate to analyze these data
using the methods of inference discussed in
this chapter? Explain.
Chapter 24 #6
c) Create a 90% confidence interval for the difference in mean pulse rates.
i) Parameter of interest
The parameter of interest is the difference in the mean pulse rates for men, 𝝁𝑴
, and women, 𝝁𝑭 .
Chapter 24 #6
c) Create a 90% confidence interval for the difference in mean pulse rates.
ii) Assumptions and conditions (You did this in part b.)
iii) Name the interval
Since the conditions are met, I will create a two sample t-interval with
40.2 degrees of freedom.
Chapter 24 #6
c) Create a 90% confidence interval for the difference in mean pulse rates.
iv) Interval
Chapter 24 #6
d) Does the confidence interval confirm your answer to part a? Explain.
Chapter 24 #14
Chapter 24 #14
a) Find 95% confidence intervals for the average number of pegs that males and females
can each place. (“I” only. Don’t worry about “PAN C” for this.)
Chapter 24 #14
b) Those intervals overlap. What does this suggest about any gender-based difference in
manual agility?
Chapter 24 #14
c) Find a 95% confidence interval for the difference in the mean number of pegs that could
be placed by men and women. (“I” only. Don’t worry about “PAN C” for this.)
Chapter 24 #14
d) What does this interval suggest about any gender-based difference in manual agility?
Chapter 24 #14
e) The two results seem contradictory. Which method is correct: doing two-sample
inference, or doing one-sample inference twice?
Chapter 24 #14
f) Why don’t the results agree?
Chapter 24 #20
Chapter 24 #20
a) At the meeting of the marketing staff, you have to explain what this output means. What
will you say?
Chapter 24 #20
b) What advice would you give the company about the upcoming ad campaign?
Chapter 24 #24
Chapter 24 #24
a) Explain what “statistically significant” means in this context.
Chapter 24 #24
b) If their conclusion is incorrect, which type of error did the researchers commit?
Chapter 24 #24
c) Does this prove that using the internet at home can improve a student’s performance in
science? (Think. What type of study in this?)
Chapter 24 #16 – Notes Only
Chapter 24 #16 – Notes Only
a) Test appropriate hypotheses and state
your conclusion.
The parameter of interest is the difference in the mean mortality rate for two
locations:
1) North of Derby, 𝝁𝑵
2) South of Derby, 𝝁𝑺
𝑯𝟎 : 𝝁𝑵 − 𝝁𝑺 = 0
𝑯𝟎 : 𝝁𝑵 − 𝝁𝑺 ≠ 0
Chapter 24 #16 – Notes Only
a) Test appropriate hypotheses and state
your conclusion.
Independence is reasonable because,
the 34 towns North of Derby can be considered representative of all towns in that region
and 34 towns is less than 10% of all towns in that region as long as there are at least 340
towns in the region and
the 27 towns South of Derby can be considered representative of all towns in that region
and 27 towns is less than 10% of all towns in that region as long as there are at least 270
towns in the region.
Chapter 24 #16 – Notes Only
a) Test appropriate hypotheses and state
your conclusion.
The samples from each region are independent of each other.
We cannot create boxplots without data and the samples are only moderate in size. Since
we cannot check the Nearly Normal Condition, we will proceed with caution and perform
a two sample t-test with 53.5 degrees of freedom.
Chapter 24 #16 – Notes Only
a) Test appropriate hypotheses and state
your conclusion.
𝒕𝟓𝟑.𝟓 =
𝟏𝟔𝟑𝟏.𝟓𝟗 −𝟏𝟑𝟖𝟖.𝟖𝟓
𝟑𝟕.𝟓𝟒𝟔
= 6.47
P-value = 2P(𝒕𝟓𝟑.𝟓 > 6.47 ) = 3.2 x 𝟏𝟎−𝟖
With a P-value well below 5%, we will reject the null hypothesis.
Chapter 24 #16 – Notes Only
a) Test appropriate hypotheses and state
your conclusion.
With a P-value well below 5%, we will reject the null hypothesis.
There is sufficient evidence to say that the difference in mortality
rates between the region North of Derby and South of Derby is not
the same. There is a significant difference in mortality rates in the
two regions.
Chapter 24 #16 – Notes Only
Chapter 24 #26 –
Chapter 24 #26 –
a. Do women or men appear to be faster at swimming across the lake? Support your answer
by interpreting a confidence interval. (Don’t worry about PANIC. Assume all assumptions
are met and create your interval. Then answer the question using the results of your
interval.)
Chapter 24 #26 –
b. Vikki Kieth was responsible for two of the more remarkable crossings, but she also swam
Lake Ontario two other times. In fact, of the 36 crossings in this analysis, 7 were repeat
crossings by a swimmer who’d crossed the lake before. How does this fact affect your thoughts
about the confidence interval. (HINT: Think about the “A” in “PANIC”.)