Question

Autism may be marked by different patterns of brain growth during early life. Researchers measured brain volume (in milliliters, using an MRI) in 28 boys who were later diagnosed with autism. Brain volume is also available for 14 boys who did not develop autism; these 14 boys serve as the control group. The sample statistics are presented for both groups in the table below. Assume that the population variances are equal. Use a sigificance level of 0.05 to test for a difference between the autism and control groups.

Groups | Sample size | Sample mean | Sample SD |

Autism (group 1) |
n_{1} = 28 |
y_{1} = 1213.53 |
s_{1} = 87.94 |

Control (group 2) |
n_{2} = 14 |
y_{2} = 1093.95 |
s_{2} = 69.38 |

3. The standard error of the estimated difference between the autism and control groups is (give answer to 4 places after decimal)

4. The value of the test statistic is (give the answer to 4 places after decimal):

5. The P-value is approximately:

6. According to the P-value method, what decision would you
make?

Because P-value < α, I reject H_{0}.

Because P-value > α, I reject H_{0}.

Because P-value < α, I fail to reject H_{0}.

Because P-value > α, I fail to reject H_{0}.

7. If you incorrectly reject the Null hypothesis, what type of
error did you make?

None. If I correctly followed the rejection rule I would not make
an error.

Type-I error

Type-II error

8. The 90% confidence interval for the true difference between brain volumes is (give answers to two places after decimal):

lower bound: upper bound:

Answer #1

Autism may be marked by different patterns of brain growth
during early life. Researchers measured brain volume (in
milliliters, using an MRI) in 29 boys who were later diagnosed with
autism. Brain volume is also available for 13 boys who did not
develop autism; these 13 boys serve as the control group. The
sample statistics are presented for both groups in the table below.
Assume that the population variances are equal. Use a sigificance
level of 0.05 to test for...

Autism may be marked by different patterns of brain growth
during early life. Researchers measured brain volume (in
milliliters, using an MRI) in 27 boys who were later diagnosed with
autism. Brain volume is also available for 15 boys who did not
develop autism; these 15 boys serve as the control group. The
sample statistics are presented for both groups in the table below.
Assume that the population variances are equal. Use a significance
level of 0.05 to test for...

To investigate if autism is marked by different brain growth
patterns in early life, studies have tried to link brain size in
infants and toddlers to autism. Suppose the whole-brain volume in
non-autistic toddlers is known to be 1200 milliliters, on average.
One study based on a sample size of 25 autistic toddlers had a
sample mean volume of 1280 ml with a standard deviation of 230
ml.
a.Calculate a 95% confidence interval for the whole-brain volume
of autistic toddlers....

In the journal Mental Retardation, an article reported the
results of a peer tutoring program to help mildly mentally retarded
children learn to read. In the experiment, the mildly retarded
children were randomly divided into two groups: the experimental
group received peer tutoring along with regular instruction, and
the control group received regular instruction with no peer
tutoring. There were n1 = n2 = 36 children in each group. The
Gates-MacGintie Reading Test was given to both groups before
instruction...

In the journal Mental Retardation, an article reported
the results of a peer tutoring program to help mildly mentally
retarded children learn to read. In the experiment, the mildly
retarded children were randomly divided into two groups: the
experimental group received peer tutoring along with regular
instruction, and the control group received regular instruction
with no peer tutoring. There were n1 =
n2 = 30 children in each group. The
Gates-MacGintie Reading Test was given to both groups before
instruction...

In an experiment on relaxation techniques, subjects’ brain
signals were measured before and after the relaxation exercises
with the following results:
Person
1
2
3
4
5
Before
31
38
62
52
28
After
27
36
58
49
24
Assuming the population is normally distributed, is there
sufficient evidence to suggest that the relaxation exercise slowed
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a. This is a:
z-test for one proportion
t-test for the mean
t-test for matched pairs
z-test for the...

A group of researchers wants to examine whether taking multiple
practice quizzes improve scores on tests. They compare the exam
scores for a sample of n1 = 12 students who
took multiple practice quizzes with the test scores of a sample of
n2 = 10 students who did not do any practice
quizzes. Results of the study revealed that the practice quiz group
had M1 = 95, SS1 = 52. The
no quiz group had M2 = 92,
SS2 =...

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...

1a)
A researcher conducts an independent-measures study to examine
how the brain chemical serotonin is related to aggression. One
sample of rats serves as a control group and receives a placebo
that does not affect normal levels of serotonin. A second sample of
rats, low serotonin group, receives a drug that lowers brain levels
of serotonin. Then, the researcher tests the animals by recording
the number of aggressive responses each of the rats display. See
the data below. Is there...

In the journal Mental Retardation, an article reported
the results of a peer tutoring program to help mildly mentally
retarded children learn to read. In the experiment, Form 2 of the
Gates-MacGintie Reading Test was administered to both an
experimental group and a control group after 6 weeks of
instruction, during which the experimental group received peer
tutoring and the control group did not. For the experimental group
n1 = 30 children, the mean score on the
vocabulary portion of...

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