Question

A random sample of 247 domestic flights provided by Raven Airways found that 91% of them arrived on time. A random sample of 235 domestic flights provided by Osprey Airlines found that 85% of them arrived on time. Perform a significance test at α = 0.05 to determine if a significantly higher proportion domestic flights arrive on time for Raven Airways than for Osprey Airlines. State your hypotheses, find the test statistic and p-value, and state your

conclusion.

a) What are the hypotheses for this test?

2. b) Value for p̂pooled =

c) Value of the numerator of zT =

d) Value of the denominator of zT =

e) Final value of zT =

2. f) P-value =

2. g) How does the p-value compare to

2. h) Write your conclusion for the test:

Answer 1

a)

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

b)

p1cap = 0.91
p1cap = 0.85
pcap = (X1 + X2)/(N1 + N2) = (0.91*247+ 0.85*235)/(247+235) = 0.8807

c)
(0.91-0.85) = 0.06

d)

sqrt(0.8807*(1-0.8807)*(1/247 + 1/235)) = 0.0295

e)

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.91-0.85)/sqrt(0.8807*(1-0.8807)*(1/247 + 1/235))
z = 2.03

f)

P-value Approach
P-value = 0.0207

g)

As P-value < 0.05,

h)

reject the null hypothesis.