Stat 281: Intro to Statistics
F2005, Dr. Galster
Final Practice
Name__________________
1. Terms:
population, sampling frame, sample
parameter, statistic
measurement scales (nominal, ordinal, interval, ratio)
numeric (quantitative) vs categorical (qualitative, class, attribute) variables
continuous & discrete variables
measures of dispersion (range, MAD, variance, standard deviation)
measures of central tendency (mean, median, mode)
expected value
percentiles
events (complementary, mutually exclusive, exhaustive, independent)
commonly used symbols, for example, sx .
Central Limit Theorem
confidence interval, hypothesis test, confidence level, level of significance
rejection region, p-value
type I error, type II error, power
shapes of distributions/histograms (normal, symmetric, skewed right/left, uniform)
correlation, linear relationship (positive, negative, none)
best fit line (equation) or least squares line (equation)
2. Calculate probabilities in
various discrete distributions (table of values, tree diagram, urn problems, dice)
binomial distribution
normal distribution
3. Build confidence intervals and conduct hypothesis tests
one-sample mean (t, z)
one-sample proportion (z)
one-sample variance (chi-square)
two-sample paired t
two-sample independent t
4. Answer questions about correlation and regression similar to last homework.
Some Sample Questions
5. A number calculated from a sample and often used to estimate population
characteristics is a ___statistic______.
6. The median is popular as a measure of central tendency when the data tend to have
extreme outliers, as such outliers have a big influence on the mean.
7. A number that summarizes, or reveals a characteristic of, the population or
distribution is a ___parameter___.
8. Whenever events have no outcomes in common they are called _mutually__
_exclusive__.
9. Tell what it means for two events to be independent (describe, don’t give formula).
The occurrence of one event gives no information about the probability of the other.
10. How do you decide what the null and alternative hypotheses are?
The null hypothesis is generally the status quo, current theory, or the conclusion that
you would use if the evidence wasn’t persuasive. The alternative hypothesis usually
involves what you would like to prove, or the conclusion that requires the burden of
proof before it will be accepted (like a guilty verdict).
11. Failing to reject a null hypothesis when it is false is a _Type II___ error.
12. The p-value of a test is calculated, for a two-tailed test, by finding the probability of
the tail further out than the test statistic, then doubling it.
13. The graph, right, shows a distribution that is
a. Normal
b. Skewed Left
c. Skewed Right
d. Uniform
14. A discrete distribution has values that
a. are very hard to find because they’re so secretive.
b. consist of distinct numbers separated by gaps.
c. are a finite set.
15. The symbol commonly used for the standard deviation of the population is
a. x .
b.  .
c. sx .
d.  .
16. The justification for saying that x is normally distributed if n is large enough
a. is due to the Central Limit Theorem.
b. comes from the Continuous Distribution Law.
c. may not be applicable to all distributions of X.
d. is thought to be a result of a communist plot during the 1950’s
17. The confidence level of an interval estimate is
a. the probability that μ is in the interval.
b. the percent of sample means that are in the interval.
c. the percent of such intervals that would contain the parameter in the long run.
d. the amount of confidence we feel in our estimation procedure.
18. The purpose of the null hypothesis is
a. to state what the experiment is about.
b. to state what is currently believed.
c. to give a reason for rejecting the alternative.
d. to state the research hypothesis in statistical terms.
19. Refer to the graph below. Does the data display a linear relationship? Would the
correlation be positive, negative, or zero? Yes, negative
95
Output
85
75
65
55
10
15
20
25
30
35
40
45
50
55
Input
20. The value of r (correlation coefficient) for the graph below is approximately
a. -0.5
b. 0
c. 0.2
d. 0.9
y 5
4
3
2
1
0
0
1
2
3
4
5
x
21. The following data were collected from a sample. Complete the table.
Obs
1
2
3
Sums
x
x
1
2
5
8
8/3
xx
-5/3
-2/3
7/3
0
MAD
22. Suppose P(A)=.8, P(B)=.4 and P(A∩B)=.2.
|xx|
5/3
2/3
7/3
14/3
14/9
Variance
Standard
Deviation
(x  x)2
25/9
4/9
49/9
78/9
13/3
2.08
a. What is P(AUB)? 1
b. Are A and B independent? No, P(A)P(B)=.31, not .2
c. Are A and B mutually exclusive? No, the intersection is not empty
d. What is the probability of A complement? .2
23. Suppose an urn contains one Blue marble, one Red marble, and two White marbles.
Suppose two marbles are drawn in sequence, setting the first aside before drawing the
second. Make a tree diagram to illustrate the sample space and calculate the
probability of getting two marbles of different colors.
P(different colors)=5/6.
24. Find the probabilities from a normal distribution with μ=10 and σ2=4.
a. P(4<X<12) .8400
b. P(X<6) .0228
25. Let X be a random variable representing the height of a stalk of corn. If heights of
corn plants are normally distributed, with a mean of 86 inches and a standard
deviation of 8 inches, describe the distribution of the sample mean, if the sample
consists of 16 plants.
Since X is normally distributed, so is X-bar. It has a mean of 86 inches and a
standard deviation of 2 inches.
26. Write appropriate null and alternative hypotheses for the following scenarios:
a. The average pulling power of flying reindeer has been 6500 wurps. Santa
would like to know if his current herd has an improved average.
Ho: μ=6500
Ha: μ>6500
b. Do female voters tend to favor Democratic candidates for president?
Let p be the proportion of female voters who favor the Democrat. Then
Ho: p=.5
Ha: p>.5
27. 25 randomly selected compact cars were tested for gas mileage. The mean was 32
mpg and the sample standard deviation was 5. Assume gas mileages are normally
distributed. Find a 90% confidence interval for the mean gas mileage of compact
cars.
32  t ( 24,.05) 5 / 25
32  1.71
(30.29,33.71)
28. Records of students from two schools were randomly selected and the GPA’s were
recorded. 30 students from one school had an average GPA of 2.7, with a standard
deviation of 0.8, and 40 students from a second school had a average GPA of 3.1,
with a standard deviation of 0.7. Conduct a test, using a significance level of .10, to
determine if there is a difference between the average GPA’s of the two schools.
Assume the populations are normal and the variances are the same.
1. H0: μ1=μ2
Ha: μ1≠μ2
2. This is a test of difference of means, with large enough samples to assume sample
means are normal, but sigma is unknown, so use t* for difference of means with the
pooled variance formula.
3. Reject H0 if t*>t(68, .05)=1.67 or if t*<-1.67.
sP
4.
2
n1  1  s12   n2  1  s2 2


t* 
(n1  1)  (n2  1)
( x1  x 2 )  ( 1   2 )
1 1
sP 2    
 n1 n2 


29  0.82  39  0.7 2
 .554
29  39
(2.7  3.1)  0
1 
 1
.554   
 30 40 
 2.225
5. Since t*<1.67, Reject H0 and conclude the average GPAs are different.
29. A fleet manager received a recall notice concerning a defective ignition component
that is causing trucks to stall without warning. The notice says that one out of 20 of
these components will fail within the first year of service, but there is no way to tell
which ones they will be. The fleet has ten trucks of the model named in the warning.
a. What is the probability that none of the trucks will suffer this failure (in their
first year) if the part is not replaced?
P(0)=(10choose0)(.05)^0(.95)^10=.599
b. What is the probability that one will fail?
P(1)=(10choose1)(.05)^1(.95)^9=.315
c. What is the probability that more than one will fail?
P(X>1)=1-(P(0)+P(1))=1-.599-.315=.086