The manager of a travel agency is considering a new promotion plan in
order to increase sales. Currently, the mean sales rate per agent is 10 trips
per month. The correct set of hypotheses for testing the effect of the
promotion plan is
H0 : μ = 10 Ha : μ ≠ 10
H0 : μ ≤ 10 Ha : μ > 10
H0 : μ > 10 Ha : μ ≤ 10
H0 : μ ≥ 10 Ha : μ < 10
Suppose p-value is equal to 0.0626. The null hypothesis can be rejected
if α = .01
if α = .05
if α = .10
Not enough information to make a conclusion.
Which of the following statements is not true about the level of significance
for a hypothesis test?
The level of significance is denoted by alpha (α ) .
If the p-value is less than the level of significance, we reject the null
hypothesis.
The level of significance is the maximum allowable probability of
making a Type I error.
The level of significance is determined by the value of the test statistic.
z statistic; 0.0287
z statistic; 0.0574
t statistic; between 0.025 and 0.05
t statistic; between 0.05 and 0.10
Which of the following does not need to be known in order to compute the
p-value?
The level of significance
Knowledge of whether the test is one-tailed or two-tailed
The value of the test statistic
The distribution that should be used
The 95% confidence interval constructed by the sample contained 0.
The 95% confidence interval constructed by the sample did not contain
0.
The absolute value of the test statistic is less than 1.96.
The p-value must be strictly less than 0.025 (i.e., p-value < 0.025).
It is known that the mean of a population is 35. A sample of size 55 was
taken and the sample mean was 32. If H0 : μ ≤ 30 , and you decided to
reject the null hypothesis, it means
you have committed a Type I error
you have committed a Type II error
you have committed a Type III error
you have committed neither Type I nor Type II error
Using the same data set, if the null hypothesis is not rejected at the 1%
level of significance, it
may be rejected or not rejected at the 5% level of significance
will always be rejected at the 5% level of significance
will never be rejected at the 5% level of significance
should never be tested at the 5% level of significance
We have a population that is normally distributed with an unknown
variance. A two-tailed hypothesis test was conducted for the population
mean. A random sample of size 22 was selected. At α level of significance,
a student wrongly used zα/2 as the critical value and concluded to reject
the null hypothesis. If the student did not make the mistake, what would
be the correct conclusion?
The conclusion stays the same, that is, the null hypothesis should be
rejected.
The conclusion is different, that is, the null hypothesis should not be
rejected.
There is insufficient information to make a conclusion. In order words,
the null hypothesis may or may not be rejected.
None of the above.
A random sample of 100 people was taken. Fifty-five of the people in the
sample favored Candidate A. We are interested in determining whether
the proportion of people in the population in favor of Candidate A is less
than 60%. What is the value of the test statistic?
−1.005
−1.02
1.005
1.02
Based on the assumptions of an ANOVA procedure, which of the following
cannot be determined?
Whether all the population means are different.
The distributions of the populations.
Whether the samples are independent or not.
The variance of the other populations if the variance of one population
is known as 10.
H0 : μ1 −μ2 ≤ 3 can never be rejected at α = 0.05
H0 : μ1 −μ2 ≤ 5 can never be rejected at α = 0.01
H0 : μ1 −μ2 ≥ 4 can never be rejected at α = 0.05
Insufficient data to claim any of the above.
Exhibit 1:
Salary information for random samples of male and female employees in a
large company is shown below.
Refer to Exhibit 1. The 95% confidence interval for the difference between
the average salaries of male and female employees in this company is (in
$1,000)
0 to 6.92
−2 to 2
−1.96 to 1.96
−0.92 to 6.92
Exhibit 1:
Salary information for random samples of male and female employees in a
large company is shown below.
Refer to Exhibit 1. We would like to test whether the average salary of
male employees is different from that of female employees in this company.
The value of the test statistic is
2.0
1.5
1.96
1.645
Refer to Exhibit 2. What are the appropriate null and alternative
hypotheses if we want to test to determine whether the training program
increase the daily production rates?
In refer to Exhibit 2. What is the value of the test statistic?
1.342
2
3.464
1.414
Refer to Exhibit 2. At 5% level of significance, we
reject the null hypothesis
do not reject the null hypothesis
may or may not reject the null hypothesis
conclude none of the above
Refer to Exhibit 3. The total sum of squares (SST) is
64
120
184
Cannot be determined
Refer to Exhibit 3. At 5% level of significance, if we want to determine
whether or not the means of all the populations are equal, the critical
value of F is
5.69
2.53
8
1
Refer to Exhibit 3. The conclusion of the test is:
Not all the population means are equal
All the population means all equal
At least two population means are equal
Cannot be determined whether the population means are equal or not
Let A = P(−1 < X < 1) , B = P(−1 < Y < 1) , and C = P(−1 < Z < 1) , where
X ~Normal (−1,1) , Y ~ Normal(0, 2) , and Z ~ Normal(0,1) . Choose the
right inequality below:
A > B > C
C > A > B
B > C > A
A > C > B
As the sample size increases, the expected value of the sample mean
remains the same.
As the sample size increases, the 100(1 −α )% confidence interval
becomes narrower.
From a population that is not normally distributed and whose standard
deviation is unknown, a sample of 15 items is selected to develop an
interval estimate for the population mean μ . Which of the following is
true?
The sample size must be increased.
The normal distribution may be used.
The t distribution with 14 degrees of freedom can be used.
The t distribution with 15 degrees of freedom an be used.
In estimating the population mean, it is known that the necessary sample
size is 150 in order to provide a particular margin of error at 98%
confidence level. With a 95% confidence level, what is the minimum sample
size that needs to be taken if the desired margin of error is halved?
213
253
425
505
When an additional independent variable is added to the model, R2
will always increase.
Both (a) and (b) are right.
Using the least squares method, the regression line is obtained by
minimizing
SST: total sum of squares
SSR: Sum of squares due to the regression
SSE: Sum of squares due to the errors
none of the above
According to a model regressing a firm’s monthly sales (in thousands) of a
product on the price of that product, the 90% confidence interval on the
average monthly sales is [5.3, 7.7] if the price is $6. Which of the following
could be the 90% prediction interval for a single month sales if the price is
$6?
[4.4, 8.2]
[4.4, 8.6]
[5.9, 7.1]
[6.2,8.4]
If all the points of a scatter diagram lie on the least squares regression line
(see the figure below), then the coefficient of determination for these
variables based on this data is
0
1
either 1 or −1 , depending upon whether the relationship is positive or
negative
could be any value between −1 and 1
b0 and b1 are random variables
β0 and β1 are random variables
y and ε are random variables
In simple linear regression estimation the following plot of the residuals is
obtained. Based on thins residual plot, which of the following statements is
true regarding the assumptions on the error ε ?
The value of ε is zero.
The value of ε are dependent.
The variance of ε varies depending on the independent variable.
None of the above.
Four numbers selected from the whole numbers 0 to 10 (with repeats
allowed) that have the largest possible standard deviation are
0, 5, 5, 10
0, 0, 10, 10
0, 5, 10, 10
0, 0, 5, 10
Since the population size is always larger than the sample size, the sample
mean
can never be larger than the population mean
can never be equal to the population mean
can never be smaller than the population mean
can be smaller, larger, or equal to the population mean
In a binomial experiment, which one(s) of the following is (are) true?
(i) The probability of success in the second trial does not depend on the
outcome of the first trial.
(ii) Only two outcomes are possible in each trial.
(iii) The expected value is always greater than the variance.
(iv) The probability of success in each trial is always larger than the
probability of failure.
(i) only.
(i) and (ii).
(i), (ii) and (iii).
(i), (ii), (iii) and (iv).
The assembly times for products in a factory are normally distributed with
a mean of 15 minutes and a standard deviation of 6 minutes. What is the
probability that the assembly time of a randomly selected product will be
exactly 15 minutes?
1
0.5
0.4
0
X is normally distributed with mean μ and standard deviation σ . If
P(X < x0 ) > 0.65 , which one describes the correct relation between μ and
x0 ?
μ > x0
μ = x0
μ < x0
Cannot be determined.
A population is normally distributed with mean μ and a standard
deviation of 5. If a sample of size 25 is selected from this population, what
is the probability that the sample mean will be within ±1.5 of the
population mean?
0.4332
0.8664
0.9544
Since μ is not given, the probability cannot be determined.
Suppose the population standard deviation is known. Which one of the
following is incorrect?
The wider the margin of error is, the wider the confidence interval is.
The width of a confidence interval depends on the confidence coefficient.
The larger the sample mean is, the wider the confidence interval is.
When a sample is used to construct confidence intervals, the 98%
confidence interval is always wider than the 95% confidence interval.
Regarding t-distribution, which one of the following is incorrect?
The mean can be negative.
When the degrees of freedom gets larger, the t-distribution
approximates normal distribution.
t-distribution is symmetric.
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