Download Statistics Unit Review Name For each of the following I can

Statistics Unit Review
Name ______________________
For each of the following I can statements complete the problem without using your notes. All work and answers should be shown on your own
notebook paper. Check your answers. If you completed the problem successfully without your notes, check the yes box. If you got the answer
wrong or had to refer to your notes, check the no box. You should focus your studying on the problems you checked no.
Y
1
N
I can …
I can understand the characteristics of a normal distribution.
Wildlife biologists recorded the weights of grizzly bears in 2 different populations. The normal curves represent the weights of the bears in
Population A and the weights of bears in Population B.
a. Which population has the greater mean weight? Explain your reasoning.
a.
b.
c.
d.
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b. Which population has the greater standard deviation? Explain your reasoning.
c. Explain what the difference in the standard deviations means in terms of the problem
situation.
I can use the empirical rule to estimate population percentages for a set of data that is approximately normally distributed.
A researcher recorded the birth weights of a sample of newborn babies. The average birth weight was 7.2 pounds and the standard
deviation was 0.9 pound. The birth weights follow a normal distribution.
a. Label the number line so that the curve is a normal curve and follows the properties of the
normal distribution. Include 3 standard deviations above and below the mean.
b. Determine the percent of newborns that weigh between 2 standard deviations below the
mean and 2 standard deviations above the mean.
c. Determine the percent of newborns that weight less than the mean.
d. Determine the percent of newborns that weigh between 1 standard deviation above the
mean and 3 standard deviations above the mean.
e. Approximately what percent of newborns weighed between 4.5 and 9.9 pounds?
f. Approximately what percent of newborns weighed more than 9 pounds?
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I can find the number of standard deviations a value is from the mean by calculating its standardized value.
The average number of points scored per game by the individual scoring leader in the NBA from 1953 through 2007 has a mean of 31.7
points and a standard deviation of 4.6 points. In 1953, Neil Johnston was the leading scorer in the NBA with an average of 22.3 points per
game. Find the standardized value (z-score), rounded to the nearest tenth, for 22.3 points per game. What does this standardized value tell
us about Neil Johnston’s points per game?
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I can use a table of z-scores to find areas under the curve to estimate population percentages.
The birth weights of African lions are normally distributed. The average birth weight of an African lion is 3.6 pounds with a standard deviation
of 0.4 pound.
a. What percent of newborn African lions weigh less than 3 pounds?
b. What percent of newborn African lions weigh more than 3.8 pounds?
c. What percent of newborn African lions weigh between 2.7 and 3.7 pounds?
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I can interpret population percentages in the context of data.
Marine biologists in Florida are studying the tiger shark to determine the factors that are contributing to their diminishing population. Adult
tiger sharks along the Atlantic Coast of Florida have a mean length of 11.5 feet with a standard deviation of 0.9 foot. Adult tiger sharks along
the Gulf Coast of Florida have a mean length of 11.9 feet with a standard deviation of 0.6 foot. Tiger shark lengths are normally distributed.
a. The biologists need to capture 1 more adult tiger shark at least 13 feet in length for their study. Along which coast will the researchers
have a higher probability of capturing the shark they need? Explain your reasoning.
b.
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The biologists need to capture 1 more adult tiger shark less than 10.5 feet in length in order to complete their study. Along which coast
will the researchers have a higher probability of capturing the shark they need? Explain your reasoning.
I can find percentiles using a standardized value.
The birth weights of African lions are normally distributed. The average birth weight of an African lion is 3.6 pounds with a standard deviation
of 0.4 pound.
a. Determine the birth weight of a lion cub in the 80th percentile.
b. Determine the birth weight of a lion cub in the 10th percentile.
c.
Determine the birth weight of a lion cub in the 97th percentile.
d. A lioness gives birth to one cub in the 47th percentile and 1 in the 62nd percentile. Determine the difference in the cubs’ weights.
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I can make inferences and justify conclusions from experiments.
1. A 13-year study of 1328 adults randomly selected from a population carefully monitored the personal habits and health conditions of the
participants. Personal habits included tobacco use and coffee consumption. Health conditions included incidence of stroke. Which of the
following questions about this population CANNOT be answered using data from this study?
a.
b.
c.
d.
Are coffee drinkers more likely to smoke than adults who do not drink coffee?
Does coffee consumption cause a reduction in the incidence of stroke?
Do coffee drinkers have fewer strokes than adults who do not drink coffee?
What percentage of the population are coffee drinkers?
2. “Thirty percent of American women ages 19 to 39 diet at least once a month, according to a news syndcate poll released
last November. These findings are based on telephone interviews with a random sample of women listed in the Los Angeles
telephone directory.”
Can the conclusion in this study be justified? Why or why not?
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I can determine if results from an experiment are statistically significant and justify appropriate conclusions.
David recently discovered a new route to school. He wondered if travel times were different for the two routes. He decided to do an
experiment. He randomly assigned five days to the old route and five days to the new route. He recorded the time it took each day and found
the difference in the two means to be 1 minute. The distribution below shows 200 runs of a randomization test. The mean of the distribution
is 0.03 minutes and the standard deviation of the distribution is 1.11 minutes.
Which of the following is most correct?
a. The results of the experiment are statistically significant because they lie within
the middle 95% of events that happen by chance alone.
b. The results of the experiment are statistically significant because the 1 minutes
bar is tall.
c. The results of the experiment are not statistically significant because there could
be lurking variables.
d. The results of the experiment are not statistically significant because they do not
lie in the outer 5% of what would happen by chance alone.
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I can distinguish between, justify the use of, and recognize the limitations of sample surveys, experiments, and observational
studies.
Determine whether the given method of data collection is a sample survey, an observational study, or an experiment. Explain. Then identify
the population, the sample, and the characteristic of interest.
a. A high school principal wants to determine whether students who work in groups in geometry class receive higher grades than students
who do not work in groups. He directs 5 of the geometry classes to participate in group work and 5 of the geometry classes to complete
their work individually.
b. You are curious about student interest in your school about doing volunteer work in the community. You ask 120 randomly selected
students in your school whether they are interested in doing volunteer work in the community.
c. A researcher wants to know whether female professional athletes are more prone to knee injuries than male professional athletes. She
gathers data from 6 different sports organizations that have injury records for all of their male and female professional athletes.
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I can recognize the type of sampling method based on a situation and recognize bias.
Determine the sampling method used in each.
a.
b.
c.
d.
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A professor divided his class into females and males, then randomly selected a sample of each group.
A quality control specialist tests every 100th tablet that comes off the line.
In order to get a set of data of girls’ heights, Risa uses the heights of all the girls in her class.
A city manager randomly selects four blocks in the city and surveys all of the residents of those blocks.
I can calculate and interpret confidence intervals and margins of error.
1. Five hundred teenage girsl were surveyed about the number of hours they spend each week listening to music. The sample mean was 9.2
hours and the standard deviation was 2.7 hours.
a. Determine the standard deviation of the population mean.
b. Determine a 95% confidence interval for the population mean.
2. In a random sample of 1,500 grocery shoppers, 500 said they bring their own shopping bags to the store. What is the 95% confidence
interval for the percent of grocery shoppers who brought their own bags?