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In: Statistics and Probability

A simple random sample of 100 flights of a large airline (call this airline 1) showed...

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

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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. )


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