MA396 Final Exam - Takehome Portion
Theoretical Problems
Choose any 5 of the following problems from the Larson and Marx text:
- 5.4.15
- 5.4.16
- 5.4.22
- 5.5.6
- 5.6.3
- 5.6.8
- 5.7.1
If you use maple, please hand in a copy of your maple worksheet with your answer.
Practical Problems
For each of the problems below, you may use the MA145 technology guide to perform a statistical analysis.
- You should justify your choice of method, including any assumptions made in the use of the method.
- For confidence interval problems, you should indicate whether a two-tailed, left-tailed, or right-tailed confidence interval is appropriate.
- For hypothesis testing problems, state the null and alternative hypotheses.
- If the problem does not specify a level of significance, you should choose one.
| Name | Problem 1 | Problem 2 | Problem 3 | Problem 4 | Problem 5 | Problem 6 | Problem 7 | Problem 8 | Problem 9 | Problem 10 | Problem 11 | Problem 12 | Problem 13 | Problem 14 | Problem 15 |
| Renee | #13 | #43 | #37 | #9 | #23 | #2 | #42 | #11 | #14 | #40 | #45 | #25 | #36 | #27 | #3 |
| Ryan B | #40 | #31 | #48 | #39 | #3 | #2 | #7 | #41 | #34 | #14 | #29 | #28 | #25 | #6 | #50 |
| Dana | #16 | #40 | #30 | #32 | #27 | #14 | #50 | #9 | #48 | #49 | #12 | #31 | #5 | #11 | #43 |
| Susan | #16 | #40 | #29 | #42 | #13 | #23 | #46 | #17 | #34 | #50 | #28 | #7 | #14 | #27 | #22 |
| Ryan C | #13 | #31 | #30 | #42 | #19 | #43 | #26 | #5 | #34 | #16 | #49 | #25 | #23 | #50 | #36 |
| Sean D | #12 | #14 | #2 | #1 | #19 | #7 | #44 | #41 | #8 | #10 | #15 | #4 | #42 | #36 | #30 |
| Crystal | #17 | #49 | #15 | #25 | #5 | #43 | #34 | #4 | #11 | #46 | #50 | #21 | #26 | #45 | #48 |
| Brendan | #20 | #5 | #41 | #45 | #25 | #18 | #26 | #46 | #7 | #40 | #3 | #42 | #49 | #35 | #13 |
| Holly | #40 | #30 | #11 | #49 | #9 | #39 | #35 | #13 | #8 | #18 | #29 | #42 | #21 | #5 | #16 |
| Daniella | #22 | #13 | #8 | #29 | #11 | #16 | #23 | #10 | #5 | #49 | #38 | #35 | #28 | #37 | #50 |
| Greg | #5 | #37 | #9 | #2 | #46 | #40 | #27 | #14 | #48 | #34 | #23 | #42 | #41 | #15 | #35 |
| Brian | #20 | #37 | #14 | #12 | #10 | #44 | #42 | #38 | #8 | #2 | #16 | #50 | #22 | #45 | #9 |
| Lily | #20 | #14 | #35 | #43 | #29 | #4 | #34 | #23 | #44 | #12 | #24 | #49 | #36 | #22 | #6 |
| Ryan M | #8 | #20 | #2 | #22 | #9 | #44 | #31 | #35 | #28 | #30 | #3 | #14 | #25 | #32 | #33 |
| Kevin | #1 | #25 | #6 | #34 | #50 | #37 | #38 | #35 | #46 | #44 | #19 | #21 | #9 | #31 | #23 |
| Sean M | #3 | #6 | #46 | #23 | #4 | #31 | #34 | #37 | #44 | #21 | #25 | #39 | #30 | #38 | #14 |
| Amanda | #9 | #27 | #6 | #12 | #23 | #42 | #46 | #29 | #15 | #50 | #13 | #14 | #18 | #45 | #49 |
| Craig | #5 | #2 | #30 | #26 | #12 | #33 | #8 | #36 | #49 | #39 | #9 | #17 | #10 | #6 | #25 |
| Michael | #12 | #48 | #35 | #41 | #19 | #8 | #33 | #11 | #24 | #23 | #14 | #17 | #15 | #4 | #7 |
| Lauren | #2 | #14 | #48 | #27 | #7 | #34 | #32 | #5 | #20 | #12 | #1 | #31 | #24 | #28 | #50 |
| Denise | #27 | #16 | #9 | #41 | #42 | #25 | #23 | #39 | #49 | #32 | #22 | #10 | #34 | #3 | #7 |
| Janet | #39 | #11 | #2 | #42 | #34 | #17 | #22 | #40 | #16 | #28 | #20 | #41 | #12 | #23 | #10 |
| Melissa | #18 | #4 | #8 | #21 | #42 | #43 | #22 | #12 | #15 | #36 | #37 | #26 | #39 | #46 | #41 |
| Justin | #27 | #33 | #37 | #35 | #5 | #36 | #42 | #14 | #15 | #29 | #34 | #13 | #43 | #45 | #31 |
Problem 1
In a poll conducted four weeks prior to an election on a random sample of 400 likely voters in
a large city, 186 respondents indicate that they plan to vote yes on a certain ballot question.
Calculate a 99% confidence interval for the proportion of voters who plan to vote yes in the
population.
Problem 2
Samples of 75 pyrometric cones from two production batches are subject to identical firing
conditions and the bending temperatures are recorded. For sample 1, the average bending
temperature is 1004.3 degrees with a standard deviation of 8.7. For sample 2, the
average bending temperature is 1003.1 degrees with a standard deviation of 9.6.
Does this data support the claim that the average bending temperatures of the two batches
are the same?
Problem 3
A tire manufacturer claims that extensive testing shows that their tires last an average of 60,000 miles, with a standard deviation of 3,000. A random sample of 88 tires from a nationwide truck
fleet operator found the average life of the tires to be 59,324 miles. Is this result consistent
with the manufacturer's claim?
Problem 4
A researcher counts the eggs in 52 Eastern bluebird (Sialia sialis) nests and
finds an average of 2.7. A large survey from previous years had a mean of 3.0 eggs
and a standard deviation of 0.6. Does this years sample indicate a significant decline
in the number of eggs per nest compared to last year?
Problem 5
A random sample of 62 people is given a questionnaire that asks if they have a favorable,
neutral, or unfavorable attitude towards Muslims. If 18 respond that they have an
unfavorable opinion, what is the 95% confidence interval for the proportion of the population
that has an unfavorable attitude towards Muslims?
Problem 6
A gardener wants to test the effect of a fertilizer. The gardener treats 47 tomato
plants with the fertilizer, and leaves 35 plants untreated. At the end of the season,
the average weight of tomatoes from the treated vines is 3.2 pounds with a standard
deviation of 1.8. The average weight from the untreated vines is 2.9 pounds with a
standard deviation of 2.0. Does this data support the claim that the fertilizer increases
the yield per plant?
Problem 7
Analysis of a sample of 45 deer ticks (Ixodes scapularis) from wooded area reveals the presence of the Ehrlichiosis pathogen (the Ehrlichia chaffeensis bacteria) in 17 ticks.
The CDC estimates that 18% of ticks carry the pathogen. Is the data consistent with this claim?
Problem 8
In a double-blind study of Major Depressive Disorder (MDD), 43 subjects are evaluated using the Beck Depression Inventory (BDI). Subjects then receive drug therapy with seratonin-reuptake inhibitors (SRIs). After 8 weeks of treatment, subjects are reevaluated with the BDI.
The average difference in the before and after scaled BDI scores is -1.7 with a standard
deviation of 0.8. Can we conclude that SRIs are effective in mitigating the MDD severity
as measured by the BDI?
Problem 9
Nationwide statistics for alcohol rehabilitation facilities show that after 4 weeks of
treatment, 37% of patients manage to remain abstinent for 6 weeks. Out of 42 patients released from a certain alcohol rehabilitation clinic, after 6 weeks only 12 remain abstinent. Can we
conclude statistically that this particular clinic does not perform as well as the national average?
Problem 10
Social services data on the placement of 108 children under the age of 12 in foster care
shows that in 76 cases where family counselling was not employed, the average time in
foster care was 78.1 days with a standard deviation of 21.9. In 32 cases where family
counseling was employed, the average time was 59.8 days with a standard deviation of
25.3. Does this data support the claim that family counseling reduces the time in
foster care for children under 12?
Problem 11
A study examines the number of low birth weight babies born to 56 mothers without health insurance and 33 mothers with health insurance that provides prenatal care. There were 18 low birth weight
children in the no insurance group, and 7 in the group with insurance. Does this data support
the conclusion that the availability of insurance coverage for prenatal care results in
fewer low birth weight deliveries?
Problem 12
A training program is designed to provide instruction in resume writing and interview skills.
In a pilot program, 38 out of 92 participants find employment within 8 weeks of completing
the program. Construct a 95% confidence interval for the proportion of participants that
will succeed in finding employment within 8 weeks.
Problem 13
A television network claims that a show in a certain time slot has a 23 percent share of the
viewing audience and sets advertising rates accordingly. An advertiser running a commercial during the show wants to verify that the market share is 23 percent, so a telephone survey is taken during the show. The survey calls 500 randomly selected households and finds
that 102 are tuned in to the show. Does this data support the network's audience share estimate, or should the advertiser negotiate a refund?
Problem 14
A package delivery service purchases trucks that get 15 miles per gallon in city driving according to the manufacturer. A sample of 33 trucks are tested and the average mileage is 12.1 miles per gallon with a sample standard deviation of 2.1. Does this data support the claim
that the actual mileage is less than 15?
Problem 15
A retailer has 54 stores. If the average change in same store sales from 2004 to 2005 is $3,100 per week with a standard deviation of 1211, does this represent a significant change?
Problem 16
A sample of 45 documents designed to simulate prints is exposed to indirect sunlight
for 1,000 hours. A second sample of 45 identical documents is exposed to indirect fluorescent
light for 1,000 hours. An optical instrument measures the "blackness" of the ink on a scale of
zero to 50, with 50 indicating total absorption of all colors and 0 indicating
total reflection of all colors. The blackness index for each document is measured after exposure. At the end of the experiment, the average blackness index for the
sunlight sample is 44.1 with a standard deviation of 2.8. The average blackness index for
the fluorescent sample is 46.5 with a standard deviation of 3.1. Does this data support the
claim that indirect sunlight fades documents of this type faster than indirect fluorescent
light?
Problem 17
Salinity measurements on ocean water conducted in 1960 on George's Bank average 35.2 parts per thousand with a standard deviation of 1.2. In 2005, a research group collected 128 samples
in the area and measured an average of 34.6 parts per thousand. Does this data suggest
that the salinity of this part of the Atlantic is lower in 2005 than it was in 1960?
Problem 18
A sample of 65 households with children under the age of six in a rural area of sub-Saharan Africa is provided with mosquito netting, while a control group of 42 households is not. During the next year, there are an average of 0.3 new cases of falciparum malaria with a standard deviation of 0.8 in households that received netting, and 0.5 new cases with a standard deviation of 1.0 in households not provided with netting. Does this data support the claim that the netting is
effective in reducing the incidence of this type of malaria?
Problem 19
An economic study examines the household incomes of 32 recipients of microloans in the year
before and and after a loan was received. The average difference is $1,281 with a standard
deviation of 485.1. Does this data support the conclusion that microloans increase household
income?
Problem 20
Prior to enactment of antiterror legislation published data on graduate mathematics programs indicates that on average 32.1 applications from foreign students are received each year.
Three years after the enactment of the legislation, a sample of 84 graduate programs shows
an average of 21.3 foreign applicants with a standard deviation of 12.1. Does this data
support the claim that the number of foreign applicants has decreased?
Problem 21
A researcher counts gypsy moth (Lymantria dispar) egg masses in 47 quarter-acre plots and finds an average of 34.2 egg masses with a standard deviation of 14.8. A survey from the previous season found an average of 27.1 egg masses per quarter-acre. Does the new data support the claim that the level of infestation (as measured by the average number of egg masses per quarter acre) is higher this year?
Problem 22
Analysis of a sample of 45 deer ticks (Ixodes scapularis) from wooded area reveals the presence of the Ehrlichiosis pathogen (the Ehrlichia chaffeensis bacteria) in 17 ticks.
A sample of 37 ticks taken three years earlier in the same area had 9 ticks test positive for the
bacteria. Does this data support the claim that the prevalence of the Ehrlichiosis pathogen has risen over the last three years?
Problem 23
A survey of 190 randomly selected Eucalyptus trees in Pacific Grove, California finds
an average of 13.5 monarch butterfly (Danus plexippus) egg masses per tree.
Historical records indicate that 3.4 is a reliable estimate the standard deviation of measurements of this kind. Construct 95 and 99 percent confidence intervals for the average number of
monarch butterfly egg masses per tree.
Problem 24
Archaeological evidence in the form of shell casings is recovered from the site of a late nineteenth century battle fought by Native Americans and federal troops. Ballistics analysis indicates that of 85 individual firearms believed to be used by the Native Americans, 50% were repeating rifles. If we consider these 85 weapons to be a simple random sample of the Native American firearms, construct a 95% confidence interval for the proportion of Native American firearms that were repeating rifles at the time of the battle.
Problem 25
During the tenure of a certain majority leader, members of Congress affiliated with the majority
party voted in accordance with the wishes of the majority leader 85% of the time. On the first
32 votes following the appointment of a new majority leader, conformance with the party line
was 68 percent. Considered as a random sample, do the first 32 votes suggest that the level
of conformance has changed?
Problem 26
A manufacturer of pyrometric cones chooses a sample of 75 from a large production run and
records the temperature at which they bend under identical firing conditions. The mean
temperature is 1009.4 degrees centigrade, with a standard deviation of 9.3. Test the claim that
the mean bending time for the production run is 1000 degrees.
Problem 27
A random sample of 85 federal income tax returns from a county indicates an average claim
of $412.50 in charitable contributions with a standard deviation of 51.5. A sample of 75 returns
from another county indicates has an average of $386.87 with a standard deviation of 65.7.
Does this data support the claim that the level of donation to charity is the same in both
counties?
Problem 28
In a survey 320 college students are selected at random. 142 students report that they
perform at least 2 hours per week of community service. Construct a 95% confidence interval
for the proportion of college students that volunteer at least 2 hours per week.
Problem 29
In an experiment to evaluate the effect of high temperature and humidity on stored films,
35 identical test films are stored in a climate-controlled environment while another 50 identical test films are exposed to ambient temperature and humidity. After one year,
the films are evaluated for loss of transparency using a scale that runs from 0 to 100,
100 indicating no measurable loss of transparency and 0 indicating complete loss of transparency.
The average measure for the climate-controlled films is 98.2 with a standard deviation of 0.3.
The average measure for the non climate-controlled films is 97.3 with a standard deviation of
0.5. Does this data indicate that climate control is effective in preserving transparency?
Problem 30
In 2004 a banding station captures and bands 48 members of a certain species of migratory birds and records an average weight of 32.1 grams. The following year, they capture 34 members of that species, none of which have been previously banded, and record an average weight of 30.9 grams.
Historical records indicate that the standard deviation of the weight of birds of this species is 2.1. Does this data support the claim that the population mean weight for this species is lower in the second year?
Problem 31
In a survey of 150 households relocated to temporary housing after hurricane Katrina,
118 indicate that they intend to return to the places they were living before the storm.
Compute a 99% confidence interval for the proportion of families that intend to return
to their homes.
Problem 32
In a sample of 85 households with children under the age of six in a rural area of sub-Saharan Africa, 17 reported a new case of malaria in a child under 6 within the past year. Construct
a 99% confidence interval for the proportion of households with children under the age of six
in which a new case of malaria occurred during the past year.
Problem 33
Records from a banding station indicate that in 2001, the average weight of a certain species
of bird is 18.9 grams with a standard deviation of 3.1, based on 42 individual birds. In 2005, 33 individuals from this species are captured and their average weight is 16.1 grams with a standard deviation of 2.3. Is this data consistent with the claim that the average weight in the population has not changed?
Problem 34
Ocean color is known to correlate strongly with phytoplankton levels, green indicating higher
and blue lower levels of phytoplankton. An extensive ocean color survey on George's Bank
conducted in 1996 measured an average peak absorption wavelength of 502.3 nanometers with
a standard deviation of 34.7. A color survey of 80 randomly selected grid points conducted
in 2005 found an average peak absorption wavelength of 493.1 nanometers.
Given that the wavelength of green light is 510 nm and that of blue light is 475 nm, does this data indicate a significant shift in ocean color towards blue (and therefore, a reduction in phytoplankton)?
Problem 35
In a double-blind study of Obsessive-Compulsive Disorder (OCD), 104 subjects with OCD are randomly divided into equal treatment and control groups. Subjects in one group are treated with cognitive behavior therapy (CBT) while the second group receives no treatment. After 12 weeks, 7 subjects
in the CBT group have experienced a remission of OCD, while 4 subjects in the placebo group have.
Can we conclude that patients receiving treatment are more likely to remit than those not receiving treatment?
Problem 36
In a study of the effect of long-term talk therapy on depression, 48 subjects diagnosed with
major depressive disorder (MDD) are given a modified version of the Beck Depression Inventory
(BDI) after six months and again after nine months of treatment. The mean difference between
the six month and nine month BDI scores was 3.2 with a standard deviation of 2.4. Does
this data support the claim that talk therapy beyond six months is not effective.
Problem 37
The DSM-IV Axis-V Global Assessment of Functioning Scale (GAF) is a widely used, global measure of psychological, social, and occupational functioning (American Psychiatric Association, 1994). In a longitudinal study, the mean GAF score for 36 subjects in the first year was 41.2.
Published data indicates that in the general population, the mean GAF score is 68.1 with a
standard deviation of 18.5. Can we conclude from this data that the study subjects score
significantly lower on the GAF than the general population?
Problem 38
In 2005 Hospital A performed 73 coronary bypass surgeries with an average length of stay of 6.1 days and a standard deviation of 2.3. Hospital B performed 41 similar surgeries and had an average length of stay of 7.3 days with a standard deviation of 3.0. Based on this data, do
the lengths of stay for coronary bypass surgery differ significantly for these two hospitals?
Problem 39
In a large city emergency medical services records indicate that 78% of patients transported to
emergency rooms have health insurance. In a sample of 50 patients transported to a particular
hospital, 35 were found to have health insurance. EMS claims that they do not consider insurance when deciding which emergency room they will transport a patient to. Does this data support
their claim?
Problem 40
During the tenure of a certain majority leader, a random sample of 40 votes showed that 94% of the votes cast by members of the majority party were in accordance with the preference of the majority leader. On the first 38 votes following the appointment of a new majority leader, conformance with the party line was 90%. Considered as a random sample, do the first 38 votes suggest that the level of conformance has changed?
Problem 41
A retailer compares same-store sales in the months immediately before and after an ad campaign at
52 stores and finds an average increase of $12.1 (measured in thousands of dollars per week), with a standard deviation of 6.1. Does this study support the claim that the ad campaign significantly
increased sales?
Problem 42
A survey of 85 randomly selected consumers that purchased a flat-screen television in the past year
reveals that 12 selected a particular brand. Find 95 and 99 percent confidence intervals for the
market share of that brand.
Problem 43
Data from a credit card company indicates that in a certain market, families dined out an average
of 2.3 nights per week with a standard deviation of 0.8 in 2001, and 1.9 nights per week with
a standard deviation of 0.7 in 2005. Does this data indicate a significant drop in the frequency
of dining out in this market?
Problem 44
Records from a banding station indicate that in 2004, the average weight of a certain species
of bird is 17.3 grams with a standard deviation of 2.0, based on 58 individual birds. In 2005, 73 individuals from this species are captured and their average weight is 19.1 grams with a standard deviation of 2.3. Is this data consistent with the claim that the average weight in the population has not changed?
Problem 45
Research anesthetize and tag 37 adult female polar bears, measure their weight, and fit them with radio tracking devices. The following year, they are able to anesthetize and reweigh 32 of the bears. The average change in weight is -34.5 pounds with a standard deviation of 21.4. Does this indicate a significant drop in weight for the population?
Problem 46
A sample of 90 Eucalyptus trees is selected at random in Pacific Grove, California and
the number monarch butterfly (Danus plexippus) egg masses found on each tree is counted.
The average of these counts is 7.6. A very large survey the previous year found an average
of 6.8 egg masses per tree with a standard deviation of 2.1. Does the new data suggest that the average number of egg masses per tree is significantly higher this year than last?
Problem 47
Two contractors provides training in job search skills for unemployed workers. A sample of 43 workers trained by contractor A finds that 25 found jobs within 3 months of completing the training, while 18 out of 37 trained by contractor B found jobs within 3 months. Test the claim that the two contractors are equally effective if the measure of success is the number of trainees who find work within 3 months.
Problem 48
A political polling company questions a random sample 1000 likely voters in a large city and
discovers that 457 of them plan to vote for a certain candidate. Calculate a 99% confidence
interval for the proportion of votes that the candidate expects to receive.
Problem 49
In 2004 a sample of 90 Eucalyptus trees is selected at random in Pacific Grove, California and
the number monarch butterfly (Danus plexippus) egg masses found on each tree is counted.
In 2005, the process is repeated for the same 90 trees. The average difference in the egg mass
counts for each tree is recorded, and has a mean value of -3.2 with a standard deviation of 4.5.
Does this represent a statistically significant change in the number of egg masses per tree?
Problem 50
A contractor provides training in job search skills for unemployed workers. Nationally,
56% of people who go through similar programs find jobs within 3 months. In a sample of
85 workers trained by this contractor, 38 found jobs within 3 months. Test the claim that
this contractor's success rate matches the national average.