Download The 1999 win-loss statistics for the American League East baseball

Use pages 1-3 in your lesson packet to answer each of the following questions.
1) Explain the difference between a population and a sample.
2) Describe a short plan to get a random sample of people from Saugerties.
3) List the positives and negatives of surveying.
4) Suppose you want to know people’s opinion on health care reform. Phrase the question in 2 ways that
you think might get different responses.
5) How is a controlled experiment different than an observational study?
6) Decide if a (a) survey, (b) controlled experiment, or (c) observational study would be most appropriate
for each situation.
i. See if running impacts weight
ii. See if the time of year impacts the suicidal thoughts of people with depression
iii. See how many people watch 12 or more movies a year
iv.
Determine the population of Ulster County
v. See if studying improves test grades
vi.
See if the swine flu vaccine has a negative impact on pregnant women
7) Each of the following sample methods has a flaw that leads to bias. Use arrows to match the method
with the flaw.
 Collecting a sample of 10 people to represent SHS
 Surveying the girls and boys basketball teams to collect data on the
height of SHS students
 Asking a sample of people if they “really liked” the school play.
 Putting a survey about school atmosphere in each teacher’s mailbox
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 Does not represent the population
 Wording of the Question
 Size of Sample
 Possibility of nonresponse
7.
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6.
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Jean’s scores on five mathematics tests were 98, 97, 99, 98, and 96. Her scores on five English tests
were 78, 84, 95, 72, and 79. Which statement is true about the standard deviations for the scores?
(1) The standard deviation for the English scores is greater than the standard deviation for the math
scores.
(2) The standard deviation for the math scores is greater than the standard deviation for the English
scores.
(3) The standard deviations for both sets of scores are equal.
(4) More information is needed to determine the relationship between the standard deviations.
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On a nationwide examination, the Adams School had a mean score of 875 and a standard deviation
of 12. The Boswell School had a mean score of 855 and a standard deviation of 20. In which school
was there greater consistency in the scores? Explain how you arrived at your answer.
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The term "snowstorms of note" applies to all snowfalls over 6 inches. The snowfall amounts for
snowstorms of note in Utica, New York, over a four-year period are as follows: 7.1, 9.2, 8.0, 6.1,
14.4, 8.5, 6.1, 6.8, 7.7, 21.5, 6.7, 9.0, 8.4, 7.0, 11.5, 14.1, 9.5, 8.6
What are the mean, population standard deviation, and population variance for these data, to the
nearest hundredth?
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The number of children of each of the first 41 United States presidents is given in the
accompanying table. For this population, determine the mean and the standard deviation to the
nearest tenth.
How many of these presidents fall within one standard deviation
of the mean?
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Beth’s scores on the six Earth science tests she took this semester are 100, 95, 55, 85, 75, and
100. For this population, how many scores are within one standard deviation of the mean?
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From 1984 to 1995, the winning scores for a golf tournament were 276, 279, 279, 277, 278, 278,
280, 282, 285, 272, 279, and 278. Using the standard deviation for the sample, Sx, find the percent of
these winning scores that fall within one standard deviation of the mean.
10 An electronics company produces a headphone set that can be adjusted to accommodate differentsized heads. Research into the distance between the top of people’s heads and the top of their ears
produced the following data, in inches:
4.5, 4.8, 6.2, 5.5, 5.6, 5.4, 5.8, 6.0, 5.8, 6.2, 4.6, 5.0, 5.4, 5.8
The company decides to design their headphones to accommodate three standard deviations from the
mean. Find, to the nearest tenth, the mean, the standard deviation, and the range of distances that
must be accommodated.
11 Twenty high school students took an examination and received the following scores:
70, 60, 75, 68, 85, 86, 78, 72, 82, 88, 88, 73, 74, 79, 86, 82, 90, 92, 93, 73
Determine what percent of the students scored within one standard deviation of the mean.
12 Find the mean, standard deviation, and variance for the sample of scores in the table.
How many of the scores fall within one standard deviation of the mean?
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Use a scatter plot to determine the appropriate type of regression.
Write the regression equation with coefficients rounded to the nearest thousandth.
Using your regression, predict the ice thickness to the nearest tenth if the temperature has
been below freezing for 18 days.
It is safe for a snowmobile or an ATV to go on ice when the ice is about 5 or more inches
thick. Using your regression, how many days should the temperature stay below freezing for
this to happen? Round to the nearest whole number.
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Use a scatter plot to determine the appropriate type of regression.
Write the regression equation with coefficients rounded to the nearest thousandth.
Using your how many rabbits were present on the island after 10 years?
To the nearest year, how long will it take for the population to grow to 500 rabbits?
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A real estate agent plans to compare the price of a cottage,
y, in a town on the seashore to the number of blocks, x, the
cottage is from the beach. The accompanying table shows a
random sample of sales and location data.
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Use a scatter plot to determine the appropriate type
of regression.
 Write the regression equation with coefficients
rounded to the nearest thousandth.
 Use the equation to predict the price of a cottage, to the nearest dollar, located three blocks
from the beach.
The accompanying table illustrates the number of movie theaters showing a popular film and the
film's weekly gross earnings, in millions of dollars.
Number of Theaters(x)
Gross Earnings (y)
(in millions of dollars)
7
443
455
493
530
569
657
723
1064
2.57
2.65
3.73
4.05
4.76
4.76
5.15
9.35
Write the linear regression equation for this set of data, rounding values to five decimal places.
Using this linear regression equation, find the approximate gross earnings, in millions of dollars,
generated by 610 theaters. Round your answer to two decimal places.
To the nearest whole number, Find the minimum number of theaters that would generate at least 7.65
million dollars in gross earnings in one week.
In a mathematics class of ten students, the teacher wanted to
determine how a homework grade influenced a student’s
performance on the subsequent test. The homework grade and
subsequent test grade for each student are given in the
accompanying table.
a Give the equation of the linear regression line for this set of
data. Round to the nearest hundredth.
b A student in the class tells you that his last test grade was a
85. What would you predict his homework grade would be for
that unit to the nearest integer?
c A new student comes to the class and earns a homework grade
of 78. Based on the equation in part a, what grade would the
teacher predict the student would receive on the subsequent test,
to the nearest integer?
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The accompanying table shows the number of new cases reported by the Nassau and Suffolk County
Police Crime Stoppers program for the years 2000 through 2002.
Find the equation of best fit using a power regression, rounding all values
Years
New
to the nearest thousandth.
since
Cases (y)
2000 (x)
Using this equation, find the estimated number of new cases, to the
1
457
nearest whole number, for the year 2007.
2
369
3
353
In what year will the number of new cases be down to 200 cases?
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Since 1990, fireworks usage nationwide has grown, as shown in the accompanying table, where t
represents the number of years since 1990, and p represents the fireworks usage per year, in millions
of pounds.
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Find the equation
of
the
power
regression model
for this set of data, where t is the independent variable. Round values to four decimal places.
Using this equation, determine in what year fireworks usage would have reached 99 million pounds.
Based on this power model, how many millions of pounds of fireworks would be used in the year
2008? Round your answer to the nearest tenth.
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A factory is producing and stockpiling metal sheets to be shipped
to an automobile manufacturing plant. The factory ships only
when there is a minimum of 2,050 sheets in stock. The
accompanying table shows the day, x, and the number of sheets in
stock, f(x).
Write the linear regression equation for this set of data, rounding
the coefficients to four decimal places.
Use this equation to determine the day the sheets will be shipped.
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A box containing 1,000 coins is shaken, and the coins are emptied onto a table. Only the coins that
land heads up are returned to the box, and then the process is repeated. The accompanying table
shows the number of trials and the number of coins returned to the box after each trial.
Write an exponential regression equation, rounding the calculated values to the nearest tenthousandth.
Use the equation to predict how many coins, to the nearest coin, would be returned to the box after
the eighth trial.
Use the equation to predict how many trials have gone by, to the nearest trial, when only 1 coin
remains.
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The breaking strength, y, in tons, of steel
cable with diameter d, in inches, is given in
the table below.
Write the exponential regression equation, expressing the regression coefficients to the nearest tenth.
If a steel cable has a diameter of three inches, what is its breaking strength to the nearest hundredth?
What is the diameter of a cord with a breaking strength of 200 tons? Round to the nearest hundredth
of an inch.
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The accompanying table shows wind speed and the corresponding wind chill factor when the air
temperature is 10°F.
Write the logarithmic regression equation for this set
of data, rounding coefficients to the nearest ten
thousandth.
Using this equation, find the wind chill factor, to the
nearest degree, when the wind speed is 50 miles per
hour.
Based on your equation, if the wind chill factor is 0°,
what is the wind speed, to the nearest mile per hour?
Evaluate or solve each of the following problems involving natural logarithms. Round to the nearest tenth.
14 Evaluate the following expression: ln 4.5 =
15 Evaluate the following expression: 6  ln9 =
16 Evaluate the following expression: ln12  ln 52 =
17 Evaluate the following expression:
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19
20
21
22
ln 9
=
ln 3
Solve for x: 7  2ln x  5 .
Solve for x: 100  5.2 ln x  132 .
Solve for x: 12.68  ln x  15 .
Solve for x: ln 5  ln x  3 .
Solve for x: ln x  ln 4  2 .
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