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.
Does this confidence interval convince you that the mean pain level is higher for women than for men? Explain your answer.
A) No, since 0 is not in the interval and in fact the confidence interval shows all positive values, we conclude that the mean pain level is the same for women and men.
B) Yes, since 0 is not in the interval and in fact the confidence interval shows all positive values, we conclude that the mean pain level is is higher for women than for men.
C) No, since 0 is in the interval, we conclude that the mean pain level is the same for women and men.
D) Yes, since 0 is in the interval, we conclude that the mean pain level is higher for women than men.
To determine whether the mean pain level is higher for women than for men, we can perform a hypothesis test. The null hypothesis (H0) would be that there is no difference in mean pain levels between men and women, and the alternative hypothesis (H1) would be that women have higher mean pain levels.
In this scenario, a t-test can be used to compare the means of two independent samples (women and men). We will use the following formula to calculate the t-statistic:
t = (mean1 - mean2) / sqrt((s1^2 / n1) + (s2^2 / n2))
where mean1 and mean2 are the sample means (5.6 and 4.8, respectively), s1 and s2 are the sample standard deviations (1.2 and 1.5, respectively), n1 and n2 are the sample sizes (52 and 47, respectively).
Plugging in the values, we get:
t = (5.6 - 4.8) / sqrt((1.2^2 / 52) + (1.5^2 / 47))
Calculating the t-statistic gives us a value. We can then compare this value to a critical value from the t-distribution table with degrees of freedom determined by the sample sizes.
By comparing the t-statistic to the critical value, we can decide whether to reject the null hypothesis or fail to reject it. If the t-statistic falls outside the critical value range, we reject the null hypothesis in favor of the alternative hypothesis.
Once we have determined the result of the hypothesis test, we can interpret the conclusion. If the null hypothesis is rejected, it would suggest that women have higher mean pain levels than men. Whereas, if the null hypothesis is not rejected, it would indicate that there is no significant difference in mean pain levels between women and men.
Based on the information provided, we cannot directly determine whether the confidence interval convinces us that the mean pain level is higher for women than for men. Additional calculations using the t-statistic and comparison with the critical value are necessary to confirm the conclusion.