Download Prob/Stat Spring Final Review Chapter 7: Eight chemical elements

Prob/Stat
Spring Final Review
Chapter 7:
1. Eight chemical elements do not have isotopes (different forms of the same element
having the same atomic number but different atomic weights). A random sample of 30
of the elements that do have isotopes showed a mean number of 19.63 isotopes per
element and the population a standard deviation of 18.73. Estimate the true mean
number of isotopes for all elements with isotopes with 99% confidence. Interpret your
answer.
2. For a certain urban area, in a sample of 5 months, on average 28 mail carriers were
bitten by dogs each month. The standard deviation of the sample was 3. Find the 90%
confidence interval of the true mean number of mail carriers who are bitten by dogs
each month. Assume the variable is normally distributed. Interpret your answer.
3. In a study of 200 accidents that required treatment in an emergency room, 80 occurred
at work. Find the 90% confidence interval of the true proportion of accidents that
occurred at work. Interpret your answer.
4. A random sample of 22 lawn mowers was selected, and the motors were tested to see
how many miles per gallon of gasoline each one obtained. The standard deviation of the
measurements was 2.6. Find the 95% confidence interval of the true standard deviation.
Interpret your answer.
Chapter 8:
Show all 7 steps for problems in Chapter 8.
5. Based on information from the U.S. Census Bureau, the mean travel time to work in
minutes for all workers 16 years old and older was 25.3 minutes. A large company with
offices in several states randomly sampled 100 of its workers to ascertain their
commuting times. The sample mean was 23.9 minutes, and the population standard
deviation is 6.39 minutes. At the 0.01 level of significance can it be concluded that the
mean commuting time is less for this particular company?
6. An advertisement claims that Fasto Stomach Calm will provide relief from indigestion in
less than 10 minutes. For a test of the claim, 35 individuals were given the product; the
average time until relief was 9.25 minutes. From past studies, the standard deviation of
the population is known to be 2 minutes. Can you conclude that the claim is justified?
Use P-Value and test at alpha = .05.
7. Once down to about 15, the world’s only wild flock of whooping cranes now numbers a
record 237 birds in its Texas Coastal Bend wintering ground. The average whooping
crane egg weighs 208 grams. A new batch of eggs was recently weighed, and their
weights are listed below. At alpha = 0.01, is there sufficient evidence to conclude that
the weight is greater than 208 grams?
210
210.2
208.5
209
211.6
206.4
212
209.7
210.3
8. Nationwide 13.7% of employed wage and salary workers are union members (down
from 20.1% in 1983). A random sample of 300 local wage and salary workers showed
that 50 belonged to a union. At alpha = 0.05, is there sufficient evidence to conclude
that the proportion of union membership differs from 13.7%?
9. The standard deviation of the fuel consumption of a certain automobile is hypothesized
to 4.3 miles per gallon. A sample of 20 automobiles produced a standard deviation of
2.6 miles per gallon. Is the standard deviation really less than previously thought? Use
alpha = 0.05.
10. To see whether people are keeping their car tires inflated to the correct level of 35
pounds per square inch (psi), a tire company manager selects a sample of 36 tires and
checks the pressure. The mean of the sample is 33.5 psi, and the population standard
deviation is 3 psi. Are the tires properly inflated? Use alpha = 0.10. Find the 90%
confidence interval of the mean. Do the results agree? Explain. (Find the Confidence
interval and do all 7 steps)
Chapter 9:
Show all 7 steps for problems in Chapter 9.
11. The average yearly earnings of male college graduates (with at least a bachelor’s
degree) are $58,500 for men aged 25 to 34. The average yearly earnings of female
college graduates with the same qualifications are $49,339. Based on the results below,
can it be concluded that there is a difference in mean earnings between male and
female college graduates? Use alpha = .01.
Sample mean
Population standard deviation
Sample size
Male
$59,235
8,945
40
Female
$52,487
10,125
35
12. The data show the amounts (in thousands of dollars) of the contracts for soft drinks in
local school districts. At alpha = 0.10 can it be concluded that there is a difference in the
averages? Use the P-value method.
Pepsi
46
120
80
Coca-Cola
420 285
57
500
100
59
13. In an effort to increase production of an automobile part, the factory manager decides
to play music in the manufacturing area. Eight workers are selected, and the number of
items each produced for a specific day is recorded. After one week of music, the same
workers are monitored again. The data are given in the table. At alpha = 0.05, can the
manager conclude that the music has increased production?
Worker
Before
After
1
6
10
2
8
12
3
10
9
4
9
12
5
5
8
6
12
13
7
9
8
8
7
10
14. A study found a slightly lower percentage of lay teachers in religious secondary schools
than in elementary schools. A random sample of 200 elementary school and 200
secondary school teachers from religious schools in a large diocese found the following.
At the 0.05 level of significance is there sufficient evidence to conclude a difference in
proportions?
Sample size
Lay teachers
Elementary
200
49
Secondary
200
62
15. Two large home improvement stores advertise that they sell their paint at the same
average price per gallon. A random sample of 25 cans from store Y had a standard
deviation of $4.08, and store Z had a standard deviation of $5.21 based on a sample of
20 cans. At alpha = 0.05 can we conclude that the standard deviations are different?
Chapter 10:
Answer the following questions for each problem in chapter 10.
a. Draw the scatter plot of the data. Label the axis.
b. Find the equation of the least squares regression line (line of best fit.) Define what x and y
represent.
c. Interpret the slope and y-intercept in the context of the problem.
d. Plot the least squares regression line in the scatter plot.
e. Find the value of the correlation coefficient, r, and comment on the type of relationship
between the two variables.
f.
Test the significance of the correlation coefficient at α =0.05. Show ALL 7 steps.
g. Test the significance of the correlation coefficient at α =0.05 using Table I. What does this tell
us?
h. Draw the residual plot and comment on whether or not it shows that the line of best fit is useful
for the data. Don’t forget to label the axes.
i. Find the value of the coefficient of determinant and interpret it in the context of the problem.
j. Find the value of the coefficient of non-determinant and comment on some reasons for the
unexplained variation.
k. Find the value of the standard error of the estimate. Interpret it in the context of the problem.
l. What does explained variation and unexplained variation mean in the context of this
problem?
16. School district information was examined for a random selection of states. The data
below show the number of elementary schools and the number of secondary schools for
each particular state. Is there a significant relationship between the variables? Predict
the number of secondary schools when the number of elementary schools is 300.
Elementary
Secondary
201
50
766
280
148
27
218
41
519
108
396
82
274
63
17. Listed below are the number of touchdown passes thrown in the season and the
quarterback rating for a random sample of NFL quarterbacks. Is there a significant linear
relationship between the variables? What would the QB rating be when 25 touchdowns
are scored?
TDs
QB rating
34
106
21
89
15
82
22
81
34
96
26
91
23
86
Chapter 11:
Show all 7 steps for Chapter 11.
18. The reasons that workers in the 25–54 year old category were displaced according to
the U.S. Department of Labor are listed below.
Plant closed/moved 44.8%
Insufficient work 25.2%
Position eliminated 30%
A random sample of 180 displaced workers (in this age category) found that 40 lost their
jobs due to their position being eliminated, 53 due to insufficient work, and the rest due
to the company being closed or moving. At the 0.01 level of significance are these
proportions different from those from the U.S. Department of Labor?
19. A survey was taken on how a lump-sum pension would be invested by 45-year-olds and
65-year-olds. The data are shown here. At alpha = 0.05, is there a relationship between
the age of the investor and the way the money would be invested?
Age 45
Age 65
Large
Company
stock
funds
20
42
Small
company
stock
funds
10
24
International
stock
funds
10
24
CDs or
money
market
funds
15
6
Bonds
45
24
20. A guidance counselor wishes to determine if the proportions of female high school
students in his school district who have jobs are equal to the national average of 36%.
He surveys 80 female students, ages 16 through 18, to determine if they work. The
results are shown. At alpha = 0.01, test the claim that the proportions of female
students who work are equal.
Work
Don’t work
Total
16-year-olds
45
35
80
17-year-olds
31
49
80
18-year-olds
38
42
80