Question

Each question below has multiple correct answers, and you must
select all correct answers and no incorrect answers for full
credit. You have 5 attempts per question.

a. Suppose we are testing H_{0}: μ_{1} -
μ_{2} = 0, and we commit a Type II error. Which of the
following statements are true, assuming we use α = 0.05? Select all
that apply.

We reject H_{0}We FTR H_{0}The p-value is
greater than 0.05The p-value is less than 0.05μ_{1} =
μ_{2}μ_{1} ≠ μ_{2}The difference in sample
means is statistically significantThe difference in sample means is
not statistically significant

b. Suppose we are planning to test H_{0}: μ_{1} -
μ_{2} = 0, and in truth μ_{1} = μ_{2}.
Which of the following statements are true, assuming we have not
yet collected the data and we plan to use α = 0.05? Select all that
apply.

H_{0} is trueH_{0} is falseThere is a 95% chance
that the 95% CI for μ_{1} - μ_{2} will contain
zeroThere is a 5% chance that the 95% CI for μ_{1} -
μ_{2} will contain zeroThere is a 95% chance that the
p-value will be less than 0.05There is a 5% chance that the p-value
will be less than 0.05If we reject H_{0}, we will be
committing a Type I errorIf we FTR H_{0}, we will be
committing a Type II error

c. Suppose we are testing H_{0}: μ_{1} -
μ_{2} = 0, and we get a test statistic of t = -1.19. Which
of the following statements are true, given this result and
assuming we use α = 0.05? Select all that apply

The p-value is greater than 0.05The p-value is less than 0.05The
difference in sample means is statistically significantThe
difference in sample means is not statistically significantWe
reject H_{0}We FTR H_{0}The corresponding 95% CI
should contain zeroThe corresponding 95% CI should not contain
zeroIt is possible we have committed a Type I errorIt is possible
we have committed a Type II error

Answer #1

A random sample of 49 measurements from one population had a
sample mean of 16, with sample standard deviation 3. An independent
random sample of 64 measurements from a second population had a
sample mean of 18, with sample standard deviation 4. Test the claim
that the population means are different. Use level of significance
0.01.
(a) What distribution does the sample test statistic follow?
Explain.
The Student's t. We assume that both population
distributions are approximately normal with known...

A "sleep habits" survey answered by 46 randomly selected New
Yorkers contained the question "How much sleep do you get per
night?" The sample average was 7.8 hours, with a corresponding
sample standard deviation of 0.82 hours. We want to test against
the null hypothesis that New Yorkers get, on average, 8 hours of
sleep per night. α=0.05.
a. This null hypothesis should be formally written as: (You have
two attempts at this question.)
H0: μdifference = 8
H0: μ...

Consider the computer output below.
Two-Sample T-Test and CI
Sample
N
Mean
StDev
SE Mean
1
15
54.79
2.13
0.55
2
20
58.60
5.28
1.2
Difference = μ1-μ2
Estimate for difference: –3.91
95% upper bound for difference: ?
T-test of difference = 0 (vs <): T-value = -2.93
P-value = ?
DF = ?
(a) Fill in the missing values. Use lower and upper bounds for
the P-value. Suppose that the hypotheses are H0: μ1-μ2=0 versus H1:
μ1-μ2<0.
Enter your...

A random sample of
n1 = 49
measurements from a population with population standard
deviation
σ1 = 5
had a sample mean of
x1 = 11.
An independent random sample of
n2 = 64
measurements from a second population with population standard
deviation
σ2 = 6
had a sample mean of
x2 = 14.
Test the claim that the population means are different. Use
level of significance 0.01.
(a) Check Requirements: What distribution does the sample test
statistic follow? Explain....

How productive are U.S. workers? One way to answer this question
is to study annual profits per employee. A random sample of
companies in computers (I), aerospace (II), heavy equipment (III),
and broadcasting (IV) gave the following data regarding annual
profits per employee (units in thousands of dollars).
I
II
III
IV
27.5
13.8
22.1
17.6
23.1
9.5
20.3
16.8
14.3
11.3
7.7
14.3
8.9
8.3
12.5
15.1
11.1
6.1
7.9
10.6
19.5
9.8
Shall we reject or not reject...

A random sample of companies in electric utilities (I),
financial services (II), and food processing (III) gave the
following information regarding annual profits per employee (units
in thousands of dollars).
I
II
III
49.7
55.8
38.9
43.3
25.3
37.7
32.9
41.7
10.7
27.4
29.2
32.6
38.3
39.6
15.2
36.8
42.5
20.1
Shall we reject or not reject the claim that there is no
difference in population mean annual profits per employee in each
of the three types of companies? Use...

A random sample of companies in electric utilities (I),
financial services (II), and food processing (III) gave the
following information regarding annual profits per employee (units
in thousands of dollars).
I
II
III
49.3
55.7
38.7
43.3
25.0
37.3
32.6
41.5
10.9
27.1
29.4
32.9
38.5
39.9
15.5
36.5
42.2
20.4
Shall we reject or not reject the claim that there is no
difference in population mean annual profits per employee in each
of the three types of companies? Use...

A random sample of companies in electric utilities (I),
financial services (II), and food processing (III) gave the
following information regarding annual profits per employee (units
in thousands of dollars).
I
II
III
49.3
55.7
38.7
43.3
25.0
37.3
32.6
41.5
10.9
27.1
29.4
32.9
38.5
39.9
15.5
36.5
42.2
20.4
Shall we reject or not reject the claim that there is no
difference in population mean annual profits per employee in each
of the three types of companies? Use...

The highway department is testing two types of reflecting paint
for concrete bridge end pillars. The two kinds of paint are alike
in every respect except that one is orange and the other is yellow.
The orange paint is applied to 12 bridges, and the yellow paint is
applied to 12 bridges. After a period of 1 year, reflectometer
readings were made on all these bridge end pillars. (A higher
reading means better visibility.) For the orange paint, the mean...

How productive are U.S. workers? One way to answer this question
is to study annual profits per employee. A random sample of
companies in computers (I), aerospace (II), heavy equipment (III),
and broadcasting (IV) gave the following data regarding annual
profits per employee (units in thousands of dollars).
I (27.6;23.1;14.7;8.9;11.9)
II (13.1;9.9;11.7;8.1;6.9;19.5)
III ( 22.4;20.2;7.4;12.9;7.7)
IV (17.6;16.8;14.4;15.7;10.7;9.4)
Shall we reject or not reject the claim that there is no
difference in population mean annual profits per employee in each
of...

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