In: Statistics and Probability
A simple random sample of 100 flights of a large airline (call this airline 1) showed that 64 were on time. A simple random sample of 100 flights of another large airline (call this airline 2) showed that 80 were on time. Let p1 and p2 be the proportion of all flights that are on time for these two airlines.
21.Suppose we wish to conduct the test at a 10% significance level. What would our decision be? Based on that decision, what type of mistake could we have made?A)Do not reject H0, Type I errorB)Do not reject H0, Type II errorC)Reject H0, Type I errorD)Reject H0, Type II error
Result:
A simple random sample of 100 flights of a large airline (call this airline 1) showed that 64 were on time. A simple random sample of 100 flights of another large airline (call this airline 2) showed that 80 were on time. Let p1 and p2 be the proportion of all flights that are on time for these two airlines.
21.Suppose we wish to conduct the test at a 10% significance level. What would our decision be?
Two sample proportion test
Ho: P1 = P2 H1: P1 ≠ P2
p1=64/100=0.64
p2=80/100 =0.80
P = (x1+x2)/(n1+n2)
=144/200 =0.72
=-2.5198
Table value of z at 0.10 level = 1.645
Rejection Region: Reject Ho if z < -1.645 or z > 1.645
Calculated z = -2.5198 falls in the rejection region
The null hypothesis is rejected
There is enough evidence to conclude that the proportion of all flights that are on time for these two airlines are significantly different.
Z Test for Differences in Two Proportions |
|
Data |
|
Hypothesized Difference |
0 |
Level of Significance |
0.1 |
Group 1 |
|
Number of Items of Interest |
64 |
Sample Size |
100 |
Group 2 |
|
Number of Items of Interest |
80 |
Sample Size |
100 |
Intermediate Calculations |
|
Group 1 Proportion |
0.64 |
Group 2 Proportion |
0.8 |
Difference in Two Proportions |
-0.16 |
Average Proportion |
0.7200 |
Z Test Statistic |
-2.5198 |
Two-Tail Test |
|
Lower Critical Value |
-1.645 |
Upper Critical Value |
1.645 |
p-Value |
0.0117 |
Reject the null hypothesis |
Based on that decision, what type of mistake could we have made?
C)Reject H0, Type I error
( Note: A TYPE I Error occurs when we Reject Ho when, in fact, Ho is True. )