Question

A research team is interested in the effectiveness of hypnosis
in reducing pain. The responses from 8 randomly selected patients
before and after hypnosis are recorded in the table below (higher
values indicate more pain). Construct a 90% confidence interval for
the true mean difference in pain after hypnosis.

Pre |
9.4 | 13.5 | 9.5 | 13.0 | 9.9 | 7.0 | 7.1 | 7.9 |

Post |
8.6 | 8.8 | 9.9 | 8.1 | 10.8 | 12.0 | 7.4 | 9.4 |

Difference |

a) Fill in the missing table cells for the pain level differences.
Compute the differences as 'Pre - Post'.

b) If the hypnosis treatment is effective in reducing pain, we
expect the differences (pre - post) to
be ---Select--- positive negative zero even
odd prime .

Note: For (c), (d), and (e) use 3 decimals in your answers. You
should use JMP to calculate these values.

c) The point estimate for the true average effect that hypnosis has
on pain perception (i.e. *x*_{d})
is:

d) The point estimate for the true standard deviation of the effect
that hypnosis has on pain perception (i.e.
s_{d})is:

e) The standard error for the mean difference in pain scores
is:

f) For this problem, the sample size is small enough that
approximating the critical value as being t = 2 will induce
substantial error. It turns out that, for a sample size of n = 8,
the 95% t-critical value is about t = 2.4. Using this, this 95%
confidence interval for the true mean difference in pain level
after hypnosis is:

IMPORTANT: don't enter the 95% CI JMP gives you. It will be wrong,
because t-critical = 2.4 has been rounded to the nearest decimal,
while JMP uses a more precise value. You need to calculate this
yourself using the CI formula.

< *μ*_{d} <

(round your answer to 2 decimals)

g) Based on your confidence interval in part (f), does the data
seem to suggest strong evidence that this form of hypnosis has an
effect on pain? Why or why not?

(You have two attempts.)

No, because 0 is in the confidence interval for the true mean difference.No, because 0 is not in the confidence interval for the true mean difference. Yes, because 0 is in the confidence interval for the true mean difference.Yes, because 0 is not in the confidence interval for the true mean difference.No, because the sample mean difference is in the confidence interval for the true mean difference.No, because the sample mean difference is not in the confidence interval for the true mean difference.Yes, because the sample mean difference is in the confidence interval for the true mean difference.Yes, because the sample mean difference is not in the confidence interval for the true mean difference.

Answer #1

a)

differences are given in difference column

b) If the hypnosis treatment is effective in reducing pain, we expect the differences (pre - post) to be positive

c) point estimate for the true average effect that hypnosis has on pain perception =0.288

d)

point estimate for the true standard deviation of the effect that hypnosis has on pain perception =3.260

e) The standard error for the mean difference in pain scores is =1.153

f)

95% CI = -2.48 < *μ*_{d} < 3.05

g)

No, because 0 is in the confidence interval for the true mean difference.

A research team is interested in the effectiveness of hypnosis
in reducing pain. The responses from 8 randomly selected patients
before and after hypnosis are recorded in the table below (higher
values indicate more pain). Construct a 90% confidence interval for
the true mean difference in pain after hypnosis.
Perceived pain levels 'Pre' and 'Post' hypnosis for 8
subjects
Pre
6.7
11.6
12.8
12.2
10.8
15.6
10.6
10.3
Post
8.4
10.0
9.3
9.2
10.4
9.5
9.9
7.7
Difference
a) Fill...

A study was conducted to measure the effectiveness of hypnotism
in reducing pain. The measurements are centimeters on a pain scale
before and after hypnosis. Assume that the paired sample data are
simple random samples and that the differences have a distribution
that is approximately normal. Construct a 95% confidence interval
for the mean of the
"beforeminus−after"
differences. Does hypnotism appear to be effective in reducing
pain?
Before
4.9
1.9
10.9
12.1
12.4
10.7
7.6
5.4
After
6.6
2.4
7.3...

A study was conducted to measure the effectiveness of hypnotism
in reducing pain. The measurements are centimeters on a pain scale
before and after hypnosis. Assume that the paired sample data are
simple random samples and that the differences have a distribution
that is approximately normal. Construct a 95% confidence interval
for the mean of the "before−after"differences. Does hypnotism
appear to be effective in reducing pain?
Before
8.4
7.8
8.4
9.0
12.3
6.9
5.9
2.4
After
6.6
2.9
7.9
8.3...

A study was conducted to measure the effectiveness of hypnotism
in reducing pain. The measurements are centimeters on a pain scale
before and after hypnosis. Assume that the paired sample data are
simple random samples and that the differences have a distribution
that is approximately normal. Construct a 95% confidence interval
for the mean of the
"beforeminus
after"
differences. Does hypnotism appear to be effective in reducing
pain?
Before
9.2
5.6
11.5
10.9
12.2
5.0
2.6
2.4
After
6.1
2.8...

A study was conducted to measure the effectiveness of hypnotism
in reducing pain. The measurements are centimeters on a pain scale
before and after hypnosis. Assume that the paired sample data are
simple random samples and that the differences have a distribution
that is approximately normal. Construct a 95% confidence interval
for the mean of the "before minus−after" differences.
Does hypnotism appear to be effective in reducing pain?
Before 5.6, 2.5, 10.0, 7.9, 7.9, 6.8, 3.2, 6.5
After 6.5, 2.8,...

A study was conducted to measure the effectiveness of hypnotism
in reducing pain. The measurements are centimeters on a pain scale
before and after hypnosis. Assume that the paired sample data are
simple random samples and that the differences have a distribution
that is approximately normal. Construct a 95% confidence interval
for the mean of the "before minus−after" differences. Does
hypnotism appear to be effective in reducing pain?
Before
9.79.7
6.36.3
8.98.9
9.49.4
11.011.0
11.711.7
5.45.4
6.56.5
After
6.36.3
2.62.6...

A study was conducted to measure the effectiveness of hypnotism
in reducing pain. The measurements are centimeters on a pain scale
before and after hypnosis. Before 10.3 0.6 10.1 11.4 9.9 7.7 3.6
1.1 After 6.9 2.1 7.6 8.7 8.2 6.9 3.9 2.3 a. Construct a 95%
confidence interval for the mean of the "beforeminusafter"
differences. nothingless thanmu Subscript dless than nothing
(Round to two decimal places as needed.) b. Use a 0.05
significance level to test the claim that...

A study was conducted to measure the effectiveness of hypnotism
in reducing pain. The measurements are centimeters on a pain scale
before and after Hipnosis. Assume that the paired sample data are
simple random samples and that the difference is have a
distribution that is approximately normal. Construct a 95%
confidence interval for the mean of the “before – after“
differences. Does hypnotism appear to be effective in reducing
pain?
before: 9.7, 6.1, 10.7, 11.2, 12.5, 10.5, 4.9, 2.0
after:...

A study was conducted to measure the effectiveness of
hypnotism in reducing pain.The measurements are centimeters are on
a pain scale before and after hypnosis. Assume that the paired
sample data are simple random samples and that the differences have
a distribution that is approximately normal construct a 95%
confidence interval for the mean of the before – after differences.
Does hypnotism appear to be effective in reducing pain￼?
Before 8.5 4.5 8.9. 13.1. 8.0. 7.6. 1.6 0.7
After. 6.2....

An investigator wants to test the effectiveness of a new weight
loss medication at reducing BMI (kg/m2). In order for
the medication to have a high chance of receiving a sizeable
investment, the mean difference in BMI must be greater than or
equal to 5 kg/m2 in a pre/post test of BMI in
participating individuals. Suppose the following table represents
the results from a SRS of individuals enrolled in the study. Assume
a normal approximation is acceptable.
Patient
BMI Pre-Test...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 18 minutes ago

asked 20 minutes ago

asked 26 minutes ago

asked 30 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago