Question

al. 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 a=0.01 level of significance and the P-value method with the TI-84 Plus calculator. Part 1 of 4 (a) State the appropriate null and alternate hypotheses. H: p = 57 H: P8.57 This hypothesis test is a two-tailed test. Alternate Answer: Hp0.57 Hip#0.57 This hypothesis test is a two-tailed test. Part: 1 / 4 Part 2 of 4 (b) Compute the P-value. Round the answer to at least four decimal places. P-value

Answer 1

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1)

pcap = 59/82 = 0.7195
p = .57
alpha = .01

a)
Ho: p = .57
Ha: p! =.57

This hypothesis test is a two-tailed test

b) t = (pcap-p)/sqrt(p*p'/n)
= (0.7195-.57)/sqrt(.57*.43/82)
= 2.7345

b) The p-value is :
P(|t|>2.7345 at df = n-1=82-1=81)
[the t-tables can used here to convert t to cumulative probability]
= 0.0077

Answer: The p-value is 0.0077

Now, p-value of .0077 is less than alpha = .01. We reject null hypothesis.

Answer: We reject the null hypothesis and conclude that we enough evidence to say that the percentage of those with diabetes who undergo this surgery will recover from diabetes differs from 57%