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 less than 79% of those with diabetes who undergo this surgery will recover from diabetes? Use the α=0.01 level of significance and the P-value method with the TI-84 Plus calculator.

A. State the appropriate null and alternate hypotheses.

b. Compute the test statistic

c. Compute the P-value

d. Interpret the P-value.

e. State a conclusion

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.79
Alternative Hypothesis, Ha: p < 0.79

Rejection Region
This is left tailed test, for α = 0.01
Critical value of z is -2.33.
Hence reject H0 if z < -2.33

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.7195 - 0.79)/sqrt(0.79*(1-0.79)/82)
z = -1.57

P-value Approach
P-value = 0.0582

As P-value >= 0.01, fail to reject null hypothesis.

There is not sufficient evidence to conclude that less than 79% of those with diabetes who undergo this surgery will recover from diabetes