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ALGEBRA2
The lifespan of a certain brand of car tires is approximately normally distributed. The car tires have a mean lifespan of 50,000 miles and a standard deviation of 7,500 miles. What would the lifespan be for the 2.5% of the tires with the greatest lifespan in the population?
ALGEBRA2
The average lifespan of American women has been tracked, and the model for the data is $$ y = 0.2t + 73, $$ where t = 0 corresponds to 1960. What is the meaning of the y-intercept? F. In 2007, the average lifespan was 60. G. In 1960, the average lifespan was 58. H. In 1960, the average lifespan was 73. J. The lifespan is increasing 0.2 years every year.
ALGEBRA2
The lifespan of a certain brand of car tires is approximately normally distributed. The car tires have a mean lifespan of 50,000 miles and a standard deviation of 7,500 miles. What range of car tire lifespan contains the 95% closest to the mean?
SOCIOLOGY
What is the difference between lifespan and life expectancy?
EARTH SCIENCE
A star is twice as massive as the sun. How will its lifespan compare?
ALGEBRA
What is the lifespan of light bulbs that are within 2 standard deviations of the mean? Within 3 standard deviations of the mean?
ALGEBRA2
Describe what king of study you would conduct to answer each statistical question. Is the lifespan of giraffes affected by the number of offspring they produce?
VOCABULARY
Draw one line under the simple subject and two lines under the correct verb form in parentheses. The lifespan of Psittacidae (averages, average) thirty to fifty years.
PRECALCULUS
Describe the outcome if a type I or a type II error is committed when the null hypothesis is tested. The average lifespan of a goldfish is 2 years.
BIOLOGY
What relationship would you expect between a plant's lifespan and its ability to undergo secondary growth? What data could you collect to test your hypothesis? Describe an experiment to collect the data.
EARTH SCIENCE
a. What factor determines how long a star lives? b. A star is twice as massive as the sun. Will its lifespan be longer, shorter, or the same as that of the sun?
PREALGEBRA
Choose your favorite animal. Research information about that animal, such as the population over the past 10 years, the kinds of food it eats, sleeping habits, its average lifespan, average size, and average speed. Present this Information using tables and graphs.
ALGEBRA
Solve each problem using an absolute value inequality. On average, a squirrel lives to be 6.5 years old. The lifespan of a squirrel may vary by as much as 1.5 years. What is the range of ages that a squirrel lives?
PHYSICS
A human heart beats 72 times every minute. How many times, on average, does a heart beat during a healthy 70-year lifespan? (Ignore the fact that the rate at which the heart beats can vary widely with the level of physical activity.)
ALGEBRA2
A 2010 study reported that people who take long vacations tend to live longer than people who do not. One possible explanation is that vacations are good for you, improving your health and increasing your lifespan. Describe another potential explanation for the association, and identify a confounding variable.
QUESTION
For each of the following headlines identify the explanatory variable and the response variable, and suggest a possible confounding variable. Explain how the confounding variable you suggest meets the definition. "Coffee Gives Jolt to Lifespan." "Study Finds Aspirin Reduces Risk of Melanoma in Women.” "'Ecstasy' May Cause Long-Term Changes in Brain Chemistry"
PRECALCULUS
A certain brand of AAA batteries lasts an average of 13 hr, with a standard deviation of 1.2 hr. The lifespans can be described by a Normal model. The company wants to guarantee that these batteries will Inst a certain length of time. What guaranteed lifespan could be achieved by at least 96% of them?
STATISTICS
It is known that increased reproductions leads to reduced longevity for female fruitflies. Patridge and Farquhar (1981) studied whether the same phenomenon held for male fruitflies. The data are also discussed in Hanley and Shapiro (1994). The experiment set up five treatment groups, each consisting of 25 randomly assigned male fruitflies. The males in one treatment were housed with eight virgin females per day. In another treatment, the males were housed with one virgin female day. There were three control groups: males housed with eight newly impregnated females, housed with one newly impregnated female, and housed alone. (Newly inseminated females will not usually mate within two days). The data are contained in the file fruitfly, with a row for each male in the following format: Column 1: the number of females Column 2: the type of female—0 denoting newly pregnant, 1 denoting virgin, and 9 when there were no females Column 3: lifespan in days Column 4: length of thorax (mm), which is fixed at birth Column 5: percentage of time spent sleeping a. Calculate summary statistics for lifespan in each group and compare. Display the data in parallel boxplots. Qualitatively, what do you conclude? b. Do the same for percentage of time spent sleeping. c. Make a scatterplot of lifespan versus thorax length. Is thorax length predictive of lifespan and did the randomization balance thorax length between the groups? d. Use the F test to test for differences in longevity between the groups. Use both Tukey’s method and the Bonferroni method to compare all pairs of means. Summarize your conclusions. e. Repeat the analysis using the Kruskal-Wallis test and the Bonferroni method. f. How does the availability of virgin females affect the sleep of male fruitflies?
QUESTION
Each of the following headlines suggests a cause and effect conclusion but was based on an observational study. In each case, explain how you know the study was observational rather than a randomized experiment, and then rewrite the headline to be more appropriate for an observational study. "Coffee Gives Jolt to Lifespan” "Study Finds Aspirin Reduces Risk of Melanoma in Women” "'Ecstasy' May Cause Long-Term Changes in Brain Chemistry"
STATISTICS
A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. From the 28 tires surveyed, the mean lifespan was 46,500 miles with a standard deviation of 9,800 miles. Using alpha = 0.05, is the data highly inconsistent with the claim?
PHYSICS
In Bohr's theory of hydrogen, the electron in its ground state was supposed to travel in a circle of radius $5\times10^{-11}\mathrm{~m}$, held in orbit by the Coulomb attraction of the proton. According to classical electrodynamics, this electron should radiate, and hence spiral into the nucleus. Show that $v<<c$ for most of the trip (so you can use the Larmor formula), and calculate the lifespan of Bohr's atom. (Assume each revolution is essentially circular).
STATISTICS
The article “Toward a Lifespan Metric of Reading Fluency" described a study of reading speed for undergraduate and graduate students. In a sample of 24 undergraduates, the mean time to read a certain passage was 4.8 seconds, with a standard deviation of 1.9 seconds. In a sample of 24 Ph.D. students, the mean time was 2.8 seconds, with a standard deviation of 1.0 seconds. Find a 95% confidence interval for the difference in reading speed between the two groups.
QUESTION
Four possible interpretations were given for an observed association between an explanatory variable and a response variable. One of the explanations was "The response variable is causing a change in the explanatory variable.” For each of the five headlines listed below, explain whether this is a likely explanation for the observed association. "Coffee Gives Jolt to Lifespan" "Breakfast Cereals Prevent Overweight in Children" "Study Finds Aspirin Reduces Risk of Melanoma in Women" "Excessive Social Media Use Leads to Depression" "'Ecstasy' May Cause Long-Term Changes in Brain Chemistry"
ENVIRONMENTAL SCIENCE
Write your answer to each part clearly. Support your answers with relevant information and examples. Where calculations are required, show your work. The City of Philadelphia recently replaced one out of every 10 trash bins with solar-powered trash compactors. The compactor is an enclosed unit with a door that opens for trash disposal. The compactor automatically detects when the bin is full and uses a solar-powered mechanical crusher to compact the contents. When the compactor needs to be emptied, it sends an electronic signal. Use of solar-powered compactors has increased the capacity of public trash bins and has reduced the number of trash collection visits to each bin from 17 times per week to 5 times per week. (a) Describe four positive externalities of installing solar-powered trash compactors. (b) Describe six cradle-to-grave components of solar-powered trash compactors. (c) Suggest one way that the installation of solar powered trash compactors can reverse the effects of urban blight. (d) The price of a regular trash bin is $300, and it has a lifespan of 20 years. The price of a solar powered trash compactor is$4,000, and it has a lifespan of 10 years; it also requires approximately $150 in maintenance costs each year. On average, a trash collection visit costs$5 in fuel and $20 in employee salary. Based on this information, are solar-powered trash compactors economically beneficial? (e) Describe two ways that you might determine if solar-powered trash compactors are environmentally beneficial.
STATISTICS
Demographers often refer to the hazard function as the “age specific mortality rate,” or death rate. Until recently, most researchers in the field of gerontology thought that a death rate increasing with age was a universal fact in the biological world. There has been heavy debate over whether there is a genetically programmed upper limit to lifespan. Using a facility in which sterilized medflies are bred to be released to fight medfly infestations in California, James Carey and coworkers (Carey et al. 1992) bred more than a million medflies and recorded their pattern of mortality. The data file medflies, contains the number of medflies alive from an initial population of 1,203,646 as a function of age in days. Using these data, estimate and plot the age specific mortality rate. Does it increase with age?