People spend around $5 billion annually for the purchase of magnets used to trea
ID: 3226830 • Letter: P
Question
People spend around $5 billion annually for the purchase of magnets used to treat a wide variety of pains. Researchers conducted a study to determine whether magnets are effective in creating back pain. Pain was measured using the visual analog scale (VAS scaled from 0 to 1 where 1 represents 100% pain reduction and 0 represents no pain reduction), and the results given below are among the results obtained in the study--the larger the VAS, the more effective in pain reduction. 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 (similar to a placebo).
Reduction in Pain Level After Magnet Treatment: n1 = 43, x1 = 0.44, s1 = 0.039
Reduction in Pain Level After Magnet Treatment: n2 = 35, x2 = 0.43, s2 = 0.037
critical value =
test statistic =
[Select Decision]We reject the null hypothesisWe fail to reject the null hypothesisWe accept the alternate hypothesis
[Select Conclusion]With a 94% level of confidence, we can say those treated with magnets have a greater mean reduction in pain than those given a sham treatment.There is not enough evidence to suggest those treated with magnets have a greater mean reduction in pain than those given a sham treatment
*please Ti 83 or 84 calculator instructions*
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: Magnet - Placebo< 0
Alternative hypothesis: Magnet - Placebo > 0
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.06. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 0.00863
DF = 76
t = [ (x1 - x2) - d ] / SE
t = 1.16
tcritical = 1.572
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.
The observed difference in sample means produced a t statistic of 1.16. We use the t Distribution Calculator to find P(t > 1.16) = 0.125
Interpret results. Since the P-value (0.125) is greater than the significance level (0.06), we cannot reject the null hypothesis.
From the above test we do not have sufficient evidence in the favor of the claim that magnet treatment shows better results.
We fail to reject the null hypothesis.
There is not enough evidence to suggest those treated with magnets have a greater mean reduction in pain than those given a sham treatment
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.