Question

A study conducted a survey among gynecologists-obstetricians in the Flanders region and obtained 295 responses. Of those responding, 90 indicated that they had performed at least one cesarean section on demand every year. Does this study provide sufficient evidence for us to conclude that less than 35 percent of the gynecologists-obstetricians in the Flanders region perform at least one cesarean section on demand each year? Let alpha=0.05.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.35
Alternative Hypothesis, Ha: p < 0.35

Rejection Region
This is left tailed test, for α = 0.05
Critical value of z is -1.64.
Hence reject H0 if z < -1.64

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.3051 - 0.35)/sqrt(0.35*(1-0.35)/295)
z = -1.62

P-value Approach
P-value = 0.0526
As P-value >= 0.05, fail to reject null hypothesis.

There is not sufficient evidence to conclude that less than 35 percent of the gynecologists-obstetricians in the Flanders region perform at least one cesarean section on demand each year