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Analysis of Magnet Treatment of Pain

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#11. Hypothesis Test for Magnet Treatment of Pain. Researchers conducted a study to determine whether magnets are effective in treating back pain, with results given below (based on data from "Bipolar Permanent Magnets for the Treatment of Chronic Lower Back Pain: A Pilot Study," by Collacott, Zimmerman, White, and Rindone, Journal of the American Medical Association, Vol. 283, No. 10). The values represent measurements of pain using the visual analog scale. Use a 0.05 significance level to tests the claim that those given a sham treatment (similar to a placebo) have pain reductions that vary more than the pain reductions for those treated with magnets.

Reduction in pain level after sham treatment: n = 20, mean of the values in a sample = 0.44, s = 3.6

Reduction in pain level after magnet treatment: n = 20, of the values in a sample = 0.49, s = 0.96

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Sect. 8-2, p. 403. Identifying Ho and H1. In Exercises 9-16, examine the given statement, then express the null hypothesis Ho and alternative hypothesis H1 in symbolic form. Be sure to use the correct symbol ( μ, ρ, σ) for the indicated parameter.

#12 The mean top of knee height of a sitting male is 20.7 in.

H0: µ =20.7
H1: µ≠20.7

#15. Plain M&M candies have a mean weight that is at least 0.8535 g.

H0:µ = 0.8535
H1:µ > 0.8535
16. The percentage of workers who got a job through their college is no more than 2%. H0

H0: p = 0.2
H1: p < 0.2

Finding Critical Values. In Exercises 17-24, find the critical z values. In each case, assume that the normal distribution applies.
#19. Right-tailed test: α = 0.05.
Critical Z value= 1.645
20. Left-tailed test: α = 0.05.
Critical Z value = - 1.645

Sect. 8-3, p. 414 Testing Claims About Proportions. In Exercises 9-24, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s, conclusions about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method.

# 12. Travel Through the Internet. Among 734 randomly selected Internet users, it was found that 360 of them use the Internet for making travel plans (based on data from a Gallup poll). Use a 0.01 significance level to test the claim that among Internet users, less than 50% use it for making travel plans. Are the results important for travel agents?
Solution:
Null Hypothesis:

H0:

Alternative Hypothesis:
H1:

Select a level of significance
α = 0.01

Test statistic:
Z =
We obtain the result using megastat

Hypothesis test for proportion vs hypothesized value

Observed Hypothesized
0.4905 0.5 p (as decimal)
360/734 367/734 p (as fraction)
360.027 367. X
734 734 n

0.0185 std. error
-0.51 z
.3034 p-value (one-tailed, lower)

0.443 confidence interval 99.% lower
0.538 confidence interval 99.% upper
0.0475 half-width

Hence the calculated value of test statistic Z is -0.51

Conclusion:
Since the p-value (0.3034) which is greater than 0.01 we have enough evidence to accept the null hypothesis at 1% level of significance. Hence we conclude that H0:

13. (For these problems, see example on pg. 412, 413). Percentage of E-Mail Users. Technology is dramatically changing the way we communicate. In 1997, a survey of 880 U.S. households showed that 149 of them use e-mail (based on data from The World Almanac and Book of Facts). Use those sample ...

Solution Summary

The solution uses statistical analysis to determine the magnet treatment of pain. Critical values and hypothesis testing are used.

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