Answer:
Given:
Sham: n= 20, x=0.44, s=1.24,
Magnet:n= 20, x =0.49, s= 0.95
For Sham:
Sample size, n = 20
Sample mean = 0.44
Standard deviation = 1.24
For Magnet:
Sample size = 20
Sample mean = 0.49
Standard deviation = 0.95
The null and alternative hypotheses:
H0: s1²=s2²
H1: s1² ≠ s2²
a) To find the test statistics, use the formula:
Test statistics = 1.7037
b) P-value:
Sham: degrees of freedom
Magnet: degrees of freedom
The critical values:
[Za/2, df1, df2)], [(1 - Za/2), df1, df2]
![f[0.05/2, 19, 19], f[(1 - 0.05/2), 19, 19]](https://tex.z-dn.net/?f=%20f%5B0.05%2F2%2C%2019%2C%2019%5D%2C%20f%5B%281%20-%200.05%2F2%29%2C%2019%2C%2019%5D%20)
![f[0.025, 19, 19], f[0.975, 19, 19]](https://tex.z-dn.net/?f=%20f%5B0.025%2C%2019%2C%2019%5D%2C%20f%5B0.975%2C%2019%2C%2019%5D%20)
The rejection region:
Reject H0, if F < 0.3958 or if F > 2.526
c) Conclusion:
Since the critical values of test statistic is between (0.3958 < 1.7037 < 2.526), we fail to reject null hypothesis H0.
There is insufficient evidence to to support the claim that those given a sham treatment have reductions that vary more than those treated with magnets