Question

Consider a flight to be on time if it arrives no later than 15 minutes after the scheduled arrival time. Negative arrival times correspond to flights arriving earlier than their scheduled arrival time. Use the sample data to test the claim that 78.7​% of flights are on time. Use a 0.025

significance level and the​ P-value method to answer the following questions

.arrival time: 26 -34 47 -22 -15 4 -28 -24 -33 -21 -21 3 -39 22 103 -26 -39 -5 -4 -1 -44 17 -31 -42 -34 -19 -29 -22 -43 0 -27 -32 -16 -30 3 103 5 -15 25 3.

A) What are the null and alternative​ hypotheses?

B) What is the test​ statistic?

C) What is the​ P-value?

D) What is the conclusion about the null​ hypothesis?

E) What is the final​ conclusion?

Answer 1

a)
Null hypothesis, ho: 78.7​% of flights are on time
Alternative hypothesis, h1: 78.7​% of flights are NOT on time

b)
X=   33   [number of flights < 15 mins as arrival time]
n=   40   [total number of flights]
p-hat = X/n=   0.825    =33/40
po=   0.787   

test statistic, z = (phat-p)/sqrt(p*(1-p)/n)
z = (0.825-0.787)/SQRT(0.787*(1-0.787)/40)
z = 0.587

c)
p-value
2*(1-P(z<|z|)
2*(1-P(z<abs(0.586998))
normsdist(abs(0.586998))
0.5572

d)
With z = 0.587, p>5%, i fail to reject the null hypothesis and conclude that 78.7​% of flights are on time

e)
there is evidence to support that 78.7​% of flights are on time