Question

A study was conducted to determine whether magnets were effective in treating pain. The values represent measurements of pain using the visual analog scale. Assume that both samples are independent simple random samples from populations having normal distributions. Use a significance level to test the claim that those given a sham treatment have pain reductions that vary more than the pain reductions for those treated with magnets.
n xbar s
Sham 20 0.41 1.26
Magnet 20 0.46 0.93

Answer 1

Answer and Step-by-step explanation: The null and alternative hypothesis for this test are:

$H_{0}: s_{1}^{2} = s_{2}^{2}$

$H_{a}: s_{1}^{2} > s_{2}^{2}$

To test it, use F-test statistics and compare variances of each treatment.

Calculate F-value:

$F=\frac{s^{2}_{1}}{s^{2}_{2}}$

$F=\frac{1.26^{2}}{0.93^{2}}$

$F=\frac{1.5876}{0.8649}$

F = 1.8356

The critical value of F is given by a F-distribution table with:

degree of freedom (row): 20 - 1 = 19

degree of freedom (column): 20 - 1 = 19

And a significance level: α = 0.05

$F_{critical}$ = 2.2341

Comparing both values of F:

1.856 < 2.2341

i.e. F-value calculated is less than F-value of the table.

Therefore, failed to reject $H_{0}$, meaning there is no sufficient data to support the claim that sham treatment have pain reductions which vary more than for those using magnets treatment.