A new medication has been created to treat osteo-arthritis inflammation and pain. Doctors prescribing the drug claim that the drug is not as effective for women as men since women taking the medication have higher pain levels than men. The pharmaceutical company conducts a clinical trial with 52 women and 47 men having osteo-arthritis in order to determine if women taking the drug have higher pain levels than men. After treatment, the 52 women have a mean pain level of 5.6 with a standard deviation of 1.2 while the 47 men have a mean pain level of 4.8 with a standard deviation of 1.5. Higher pain level measures indicate more inflammation and pain.

Question

Test the claim that women have higher pain levels than men when taking this drug to treat osteo-arthritis. Use a 5% significance level.

Determine if the decision is Reject or Fail to reject Ho and write the conclusion for the result.

A) Reject Ho. The sample evidence does not support the claim that women have higher pain levels than men when taking this drug to treat osteo-arthritis.
B) Fail to reject Ho. The sample evidence does not support the claim that women have higher pain levels than men when taking this drug to treat osteo-arthritis.
C) Reject Ho. The sample evidence supports the claim that women have higher pain levels than men when taking this drug to treat osteo-arthritis.
D) Fail to reject Ho. The sample evidence supports the claim that women have higher pain levels than men when taking this drug to treat osteo-arthritis.

Answer 1

Ho: women's level > men's

Z = (mean1 - mean2)/standard error (SE) of difference between means

SEdiff = √(SEmean1^2 + SEmean2^2)

SEm = SD/√n

If only one SD is provided, you can use just that to determine SEdiff.

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.

I'll let you do the calculations.