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Researchers conducted a study to determine whether magnets are effective in treating back pain. The results are shown in the table for the treatment (with magnets) group and the sham (or placebo) group. The results are a measure of reduction in back pain. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below.			Treatment	Sham
μ	μ1	μ2
n	13	13
x	0.48	0.41
s	0.76	1.42

a. Use a

0.05

significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment.

What are the null and alternative hypotheses?

H0:

μ1=μ2

H1:

μ1>μ2

H0:

μ1<μ2

H1:

μ1≥μ2

H0:

μ1=μ2

H1:

μ1≠μ2

H0:

μ1≠μ2

H1:

μ1<μ2

The test statistic, t, is

nothing.

(Round to two decimal places as needed.)

The P-value is

nothing.

(Round to three decimal places as needed.)

State the conclusion for the test.

▼

Reject

Fail to reject

the null hypothesis. There

▼

is not

sufficient evidence to support the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment.

Is it valid to argue that magnets might appear to be effective if the sample sizes are larger?

Since the

▼

sample mean

sample standard deviation

for those treated with magnets is

▼

less than

equal to

greater than

the sample mean for those given a sham treatment, it

▼

is not

valid to argue that magnets might appear to be effective if the sample sizes are larger.

b. Construct a confidence interval suitable for testing the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment.

nothing<μ1−μ2<nothing

(Round to three decimal places as needed.)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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