Question

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 more than 60% of those with diabetes who undergo this surgery will recover from diabetes? Use the α = 0.05 level of significance.

(SHOW WORK PLEASE FOR ME TO UNDERSTAND THE STEPS)

1. Compute the following

p-hat, Standard error, Critical Z, and Test Z.

2. Do you reject or fail to reject the null hypothesis. Explain why. Use the α = 0.05 level of significance.

3. State the null and alternative hypotheses and what type of TEST?

4. Compute the P-value?

Answer 1

solution:

sample size = N = 82

number of patient who recover = X=59

estimated proportion = p = 0.60

step by step solution:

the null and alternative hypothesis:

it is a right tailed test

1)a) calculation of p-hat

proportion of recover patient =

b) standard error =

c) significance level =

since it is a right tailed single tailed test so we will found the critical value of a tail

critical value of z at 0.05 =

(critical value is found using z table)

d) test statistics:

4) P value = 1 - value of z to the left of 2.22

p value = 1 - 0.9868 = 0.0132

since p value 0.0132 < , we will reject the null hypothesis

conclusion: there is enough evidance to say that the more than 60% will recover