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.

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.

To determine if the decision is to reject or fail to reject the null hypothesis (Ho) in this scenario, we need to conduct a hypothesis test.

The null hypothesis (Ho) states that there is no difference in pain levels between women and men when taking this drug to treat osteo-arthritis. The alternative hypothesis (Ha) states that women have higher pain levels than men when taking this drug.

To conduct the hypothesis test, we can use a two-sample t-test since we are comparing the means of two independent samples (women and men).

1. Define the hypotheses:
- Null hypothesis (Ho): The mean pain levels of women and men when taking the drug are equal. (μw = μm)
- Alternative hypothesis (Ha): The mean pain levels of women when taking the drug are higher than those of men. (μw > μm)

2. Determine the significance level:
In this case, the significance level is given as a 5% significance level, which means alpha (α) = 0.05.

3. Calculate the test statistic:
We can use the two-sample t-test formula to calculate the test statistic:
t = (mean1 - mean2) / sqrt((s1^2/n1) + (s2^2/n2))
Where:
- mean1 and mean2 are the sample means of pain levels for women and men, respectively.
- s1 and s2 are the sample standard deviations of pain levels for women and men, respectively.
- n1 and n2 are the sample sizes of women and men, respectively.

4. Determine the critical value:
Since the alternative hypothesis is one-sided (μw > μm), we need to find the critical t-value with a 5% significance level and degrees of freedom equal to the smaller sample size minus 1 (n1 - 1).

5. Compare the test statistic with the critical value:
If the test statistic is greater than the critical value, we reject the null hypothesis. If the test statistic is less than the critical value, we fail to reject the null hypothesis.

6. Make a decision and write the conclusion:
Based on the comparison, if the test statistic is greater than the critical value, we will reject the null hypothesis (Ho). If the test statistic is less than the critical value, we will fail to reject the null hypothesis (Ho). The conclusion should be stated in terms of supporting or not supporting the claim made in the question.

With the given information, we can calculate the test statistic and compare it to the critical value to make a decision and write the conclusion.

To determine if women have higher pain levels than men when taking this drug, we can conduct a hypothesis test using the sample data provided.

The null hypothesis (Ho) states that there is no significant difference in the pain levels between women and men when taking the drug. The alternative hypothesis (Ha) states that women have higher pain levels than men.

Now, let's perform the hypothesis test using a 5% significance level.

1. Set up the hypotheses:
Ho: μw ≤ μm (Women have pain levels less than or equal to men)
Ha: μw > μm (Women have higher pain levels than men)

2. Compute the test statistic:
We can use a two-sample t-test since we are comparing the means of two independent samples.
The formula for the test statistic is:
t = (x̄w - x̄m) / sqrt((s^2w / nw) + (s^2m / nm))
where x̄w and x̄m are the sample means, sw and sm are the sample standard deviations, and nw and nm are the sample sizes.

Given:
x̄w = 5.6, x̄m = 4.8
sw = 1.2, sm = 1.5
nw = 52, nm = 47

Calculating the t-value:
t = (5.6 - 4.8) / sqrt((1.2^2 / 52) + (1.5^2 / 47))

3. Determine the critical value:
Since the alternative hypothesis states that women have higher pain levels, this is a one-tailed test.
With a significance level of 5%, the critical value for t at a degrees of freedom of 97 is approximately 1.663.

4. Decision:
If the calculated t-value is greater than the critical value, we reject the null hypothesis; otherwise, we fail to reject it.

5. Conclusion:
Based on the test statistic calculated and the critical value, we compare them to make a decision. If the calculated t-value is greater than the critical value, we reject the null hypothesis. If not, we fail to reject it.

Since I can't calculate the t-value without specific numbers, you will need to calculate it. Then, compare it to the critical value of 1.663. Once you have done that, choose the correct answer option based on the decision made.

Please let me know if you have any further questions or need clarification.