The usual treatment of hypothyroidism involves daily thyroid

The usual treatment of hypothyroidism involves daily thyroid replacement with levothyroxine (L-T4). Optimal therapy is monitored by measurement of serum TSH. The normal thyroid gland secretes both levothyroxine (L-T4) and levotriiodothyronine (L-T3). It is generally believed that treatment L-T4 alone results in normal levels of serum L-T3 to achieve a euthyroid state. Some studies suggest, however, that patients feel better when taking an L-T4/L-T3 combination compared with L-T4 alone.
Woeber (2002) wished to study this clinical issue further by evaluating the effect of L-T4 replacement therapy on serum free T4. He studied the relationship in a historical cohort of patients with chronic autoimmune thyroiditis and a group of normal individuals. Woeber\'s data gave the following results.

At the 1% level, is there a difference in the mean free T4 equal among the three groups of subjects.  Why or why not?

Is there a difference in the average ?  Explain. If needed, you may use a 95% level of confidence.

You must include in your work:
1. Test statistic, critical value or p-value, decision, and interpretation.
2. Confidence interval end points and decision.

Solution

Complete the anova table as follows:

As p value is 0.05, reject null hypothesis.

The means of all groups are not equal.