1st box- sample mean or sample standard deviation 2nd box- less than or equal to
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1st box- sample mean or sample standard deviation 2nd box- less than or equal to or greater than 3rd box- is not or is Score: 0.5 of 1 pt 3 of 9 (9 complet Hw Score: 80.56 Question Help 9.3.7-T Treatment T Sham Researchers conducted a study to determine whether magnets are effective in treating back pain. The results are u H2 shown in the table for the treatment (with magnets) group and n 30 30 the sham (or group. The results are a measure of 0.54. 0.39 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 133 s 0.65 population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts. A 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? for those treated with magnets is Since the the sample mean for those given a sham treatment, it valid to argue that magnets might appear to be effective if the sample sizes are larger click to select vour answer(s) and then click Check Answer.Explanation / Answer
State the hypotheses.
The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: 1< 2
Alternative hypothesis: 1 > 2
Note that these hypotheses constitute a one-tailed test. T
Formulate an analysis plan. For this analysis, the significance level is 0.01. 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 = 0.2703
DF = 58
t = [ (x1 - x2) - d ] / SE
t = 0.555
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 the population means, and SE is the standard error.
Since we have a one tailed test the P-value is the probability that a t statistic having 58 degrees of freedom is more than 0.555
Thus, the P-value = 0.291
Interpret results. Since the P-value (0.291) is greater than the significance level (0.01), we have to accept the null hypothesis.
Failed to reject the null hypothesis, There is not sufficient evidene to support the claim that those treated with magnets have a greater mean reduction in pain those given a sham treatment.
Since sample standard deviation for those treated with magnets is less than the sample mean for those given a sham treatment, it is valid to argue that magnets might appear to be effective if the sample size are larger.
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