Question

1. Researchers are comparing proportions of students at 2 schools that come in having not eaten breakfast. A random sample of 160 students from School 1 found that 41 had not eaten, and a separate random sample of 150 at School 2 found that 26 had not eaten. Each school has over 2000 students. Does the data give convincing evidence at that more students at School 1 come to school having not eaten breakfast than School 2? (6 Points).

H₀: _____________ H_a: _____________ =

Calculate test statistic:

P-value:

State your Conclusion:

Answer 1

p1cap = X1/N1 = 41/160 = 0.2563
p1cap = X2/N2 = 26/150 = 0.1733
pcap = (X1 + X2)/(N1 + N2) = (41+26)/(160+150) = 0.2161

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 > p2

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.2563-0.1733)/sqrt(0.2161*(1-0.2161)*(1/160 + 1/150))
z = 1.77

P-value Approach
P-value = 0.0384
As P-value < 0.05, reject the null hypothesis.

There is sufficient evidence to conclude that more students at School 1 come to school having not eaten breakfast than School 2