Problem
Curing diabetes: Vertical banded gastroplasty is a surgical procedure that reduces the volume of the stomach in order to produce weight loss. In a recent study, 82 patients with Type 2 diabetes underwent this procedure, and 59 of them experienced a recovery from diabetes. Does this study provide convincing evidence that the percentage of those with diabetes who undergo this surgery will recover from diabetes differs from $57 \%$ ? Use the $\alpha=0.01$ level of significance and the $P$-value method with the TI- 84 Plus calculator. Part: 0 / 5 Part 1 of 5 (a) State the appropriate null and alternate hypotheses. \[ \begin{array}{l} H_{0}: \square \\ H_{1}: \square \end{array} \] \[ \square<\square \quad \square>\square \quad \square=\square \] This hypothesis test is a (Choose one) $\mathbf{\nabla}$ test.
Solution
Step 1 ：The null hypothesis (H0) and the alternate hypothesis (H1) are as follows: H0: p = 0.57 (The proportion of those with diabetes who recover from diabetes after the surgery is 57%) H1: p ≠ 0.57 (The proportion of those with diabetes who recover from diabetes after the surgery is not 57%) This hypothesis test is a two-tailed test.
