Unit 11 Statistics Review
1.
2.
Estimate
the value of
the
correlation
coefficient
for each
scatter plot
in #1 & #2.
3. A survey completed at a large university asked 2,000 students to estimate the average number of hours they
spend studying each week. Every tenth student entering the library was surveyed. The data showed that the
mean number of hours that students spend studying was 15.7 per week. Which characteristic of the survey
could create a bias in the results?
1) the size of the sample
3) the method of analyzing the data
2) the size of the population
4) the method of choosing the students who
were surveyed
4. For each of the following scatter plots determine if a linear, logarithmic, exponential, or power regression would
be most appropriate.
5. The heights of a group of 1,000 women are normally distributed. The mean height of the group is 170
cm with a standard deviation of 10 cm. What is the best approximation of the number of women
between 170 cm and 180 cm tall?
(1) 950
(2) 340
(3) 680
(4) 170
1
6. Use the following set of score data to find the mean, median, mode, range, interquartile range,
population standard deviation and population variance to the nearest tenth. Then find the
probability that a randomly selected score falls within one standard deviation of the mean.
Score
60
70
75
80
90
7. After two super tankers collide at sea, an oil slick develops. The area (in square miles) of the
spill, A, after t hours is recorded and shown in the accompanying table.
a. Find a power regression equation for this data. Round your coefficients to the nearest
thousandth.
t
1.5
2
3
3.5
5
6
b. Using the regression equation found, after how many hours will the spill be 125 square
miles wide? Round your answer to the nearest tenth of an hour.
F
6
4
3
4
3
A
7.1
12.6
28.3
38.5
78.5
113
8. On your tests this year, you have received four 75’s, three 84’s, and five 92’s. Find the mean, median, and
mode of your tests. Round to the nearest tenth when necessary.
9. Find the linear regression and correlation coefficient for the
following data. Round your answers to the nearest
thousandth. What does the correlation coefficient tell you
about the relationship between the two variables?
2
10. On a standardized test, the mean is 48 and the standard deviation is 4. What percent of the scores will
fall in the range from 44 to 54? Round to the nearest percent.
11. The population, P, of a small make-believe country at 10-year intervals as shown in the accompanying
table.
t (years after 1900)
10
20
30
40
50
60
70
P (in thousands)
200 252 318 401 504 635 800
a. Draw a rough sketch of the scatter plot for this data using your calculator.
Based upon the scatter plot, what type of regression would fit the data the
best: linear, exponential, or logarithmic?
b. Find the appropriate regression, rounding your coefficients to the nearest thousandth.
c. Using the regression equation, predict the population of this country for the year 2000. Round
to the nearest thousand.
d. Determine in what year the population will exceed 2 million.
12. On a math exam, the scores of a sample of nine students from a class were 66, 81, 97, 86, 58, 76, 73,
88, and 80. Find the mean, standard deviation, and variance to the nearest tenth.
3
13. Jackie’s test scores are 87, 96, 81, and 89. What score does she need on the last test in order to
average 90 on her tests?
14. In the accompanying diagram, about 68% of the scores fall within the
shaded area, which is symmetric about the mean, x . The distribution is
normal and the scores in the shaded area range from 50 to 80. Find the
mean and the standard deviation of the scores in this distribution?
15. Susan turns on the oven and records the temperature for the first seven minutes as shown in the
accompanying table.
Time in minutes 1
2
3
4
5
6
7
Temperature
80
150
200
240
270
290
305
a. Draw a rough sketch of the scatter plot for this data using your calculator.
Based upon the scatter plot, what type of regression would fit the data the
best: linear, exponential, or logarithmic?
b. Find the appropriate regression, rounding to the nearest thousandth.
c. Using the regression equation, what will the temperature be after 8 minutes to the nearest
degree?
d. Susan is waiting for the oven to warm up to 375° so that she can start to bake a cake. Based
upon your regression, when will she be able to put the cake in the oven? Round to the nearest
minute.
4
16. A standardized test with a normal distribution of scores has a mean score of 75 and a standard
deviation of 4. If Chloe scored an 81, what would her percentile rank be to the nearest whole number?
What does this number tell you about her score?
17. Give an example of a survey, a controlled experiment, and an observational study.
18. High school enrollment for East High was recorded for the years 1950 to 1990
and is shown in the accompanying table. Determine a quadratic regression
equation that models this data, rounding coefficients to the nearest
thousandth.
Using the regression equation found, estimate the enrollment in East High in
1973 to the nearest person.
5
Years
since
1950
0
5
10
15
20
25
30
35
40
Enrollment
460
395
330
318
302
314
362
403
485