For every set of data the value of the median will always be one of the
original items of data.
If A and B are both nonempty events of a sample space S and A
and B are mutually exclusive, then A and B are dependent.
If x is a normally distributed random variable with a mean of μ and a
standard deviation of σ and if x converts to the standard score z , then
given any three of the values of x , μ , σ , and z , we can always find the
fourth value.
The t -distribution approaches the normal distribution as the number of
degrees of freedom decreases.
If the random variable Z is the standard normal score, then
Z0.65 = −Z0.35 .
The ANOVA test assumes that you sample from normal populations with
homogeneous variances.
When the F test is used to test for the equality of a set of population
means, if the null hypothesis is rejected then all of the population means
are declared to differ from one another.
In constructing a confidence interval for the mean difference in paired data
we see that as the sample size increases the width of the interval also
increases.
As the sample size increases, the sampling distribution of the sample mean
from a normal distribution has a normal curve that becomes more peaked.
Every binomial distribution may be approximated reasonably by an
appropriate normal distribution.
Which of the following is not a characteristic of a binomial probability
experiment?
Each trial has two possible outcomes: success and failure.
P(success) = 1 − P(failure)
The binomial random variable x is the count of the number of trials
that occur.
Trials are independent.
The result of one trial does not affect the probability of success on any
other trial.
In the p-value approach to hypothesis testing we reject the null
hypothesis if the:
p-value > a .
p-value ≥ a .
p-value < a .
p-value ≤ a .
p-value ≠ a .
We will want to fail to reject the null hypothesis in a chi-square test
comparing observed to expected frequencies whenever:
the observed frequencies are each approximately equal to their
corresponding expected frequency.
the observed frequencies are significantly greater than the expected
frequencies.
the observed frequencies are considerably smaller than the expected
frequencies.
all of the above.
none of the above.
Suppose we select a random sample of size n from a normal population
with a mean of μ and a standard deviation of σ and suppose k is some
number greater than μ . Which of the following is true?
None of the above can be determined without knowing specific values of
n, μ ,σ , and k .
The following is the null hypothesis in a hypothesis test for a multinomial
experiment:
H0 : P(A) = 0.15 , P(B) = 0.25 , P(C) = 0.35 , and P(D) = 0.25 .
Which of the following is the appropriate alternative hypothesis?
Ha : P(A) = 0.25 , P(B) = 0.25 , P(C) = 0.25 , and P(D) = 0.25 .
Ha : P(A) ≠ 0.15, P(B) ≠ 0.25 , P(C) ≠ 0.35, and P(D) ≠ 0.25 .
Ha : P(A) ≠ 0.15, P(B) = 0.25 , P(C) ≠ 0.35 , and P(D) = 0.25 .
Ha the probabilities are distributed differently from those listed in H0 .
Ha one of the probabilities listed in H0 is incorrect.
For a binomial distribution with five trials and 20% probability of success
per trial, what number of successes in the five trials has the highest
probability?
1
2
3
4
5
If you obtain a negative value for the chi-square statistic in a hypothesis
test, then
you will automatically rejected H0 .
you will automatically fail to reject H0 .
all expected frequencies were greater than the corresponding observed
frequencies.
all observed frequencies were greater than the corresponding expected
frequencies.
a mistake occurred in a calculation.
In comparing Student’s t-distribution to the standard normal distribution,
we see that Student’s t-distribution is:
less peaked and thinner at the tails.
less peaked and thicker at the tails.
more peaked and thinner at the tails.
more peaked and thicker at the tails.
peaked the same but thicker at the tails.
Which of the following is the probability of having the computed value of
the test statistic fall in the noncritical region when the null hypothesis is
true?
α
1 - α
β
1 - β
1 − (α +β )
If the random variable x is normally distributed with a mean of μ and
a standard deviation of σ , then P(μ +σ < x < μ + 2σ ) =
2[P(μ < x < μ + σ)]
P(μ < x < μ + σ)
P(μ - σ< x < μ - σ)
P(μ + 0.5σ< x < μ + 0.15σ)
None of these.
Which of the following probability experiments would not result in a
discrete random variable?
Observing the number of times a coin is tossed before obtaining heads.
Observing the time required for a light bulb to burn out once it is
turned on.
Observing the number of hearts when five cards are randomly selected
from a deck.
Observing the number of telephone calls coming into a switchboard in
one hour.
Observing the number of defective components in a case of 100
components.
(a) What is the probability that a randomly chosen respondent voted for the
president?
(b) What is the probability that a randomly chosen respondent is
pessimistic about the economy?
(c) What is the conditional probability that a respondent who voted for the
president will be pessimistic about the economy?
(d) What is the conditional probability that a respondent who is pessimistic
about the economy voted for the president?
(e) Are views on the economy independent of how respondents voted?
A farmer must determine whether to plant corn or wheat. If the plants
corn and the weather is warm, he earns $8000; if the plants corn and the
weather is cold, he earns $5000. If the plants wheat and the weather is
warm, he earns $7000; if he plants wheat and the weather is cold, he earns
$6500. In the past, 40% of all years have been cold and 60% have been
warm. Before planting, this farmer can pay $600 for an expert weather
forecast. If the year is actually cold, there is a 90% chance that the
forecaster will predict a cold year. If the year is actually warm, there is an
80% chance that the forecaster will predict a warm year. How can this
farmer maximize his expected profits? (10%)
Certain washing machine manufacturer (brand 1) claims that the fraction
p1 of his washing machines that need repairs in the first five years of
operation is less than the fraction p2 of another brand (brand 2). To test
this claim, we observe 200 machines of each brand, and find that 21 and 37
machines need repairs for brand 1 and brand 2 respectively. Do these data
support the manufacturer’s claim? Use α = 0.05. (5%)
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