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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]
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