According to one source, 50% of plane crashed are due at least in part to pilot

Question

According to one source, 50% of plane crashed are due at least in part to pilot error. Suppose that in a radnom sample of 100 seperate airplane accidents, 62 of them were due to pilot error.

a. Test the null hypothesis that the proportion of airplane accidents due to pilot error is not 0.50. Use significance level of 0.05.

Step 1:

Ho:

Ha:

Step 2:

One proportion z test, alpha= 0.05

Random Sample: Given

Independence: Assumed

Large Sample:

npo =

n(1-Po) =

Large popualtion=

Step 3

p=

z=

b. Choose the correct interpretation:

i. The percentage of plane crashes due to pilot error is not significantly different from 50%.

ii. The percentage of plane crashes due to pilot error is signicantly different from 50%.

Explanation / Answer

Solution:

a) Test Hypothesis:
Ho: p = 0.50
Ha: p 0.50
Here, p = po is the hypothesized or population proportion.
Accidents due to pilot errors x = 62.
number of accidents n = 100
The sample proportion of accidents due to pilot error is,
p = x/n = 62/100 = 0.62
Level of significance be = 0.05
One sample Z -test for population proportion is used to test the claim.
The test statistic:
Zobserved = p - po/sqrt(po(1-po)/n)
= 0.62- 0.50/sqrt(0.50(1-0.50)/100)
= 2.40
Find the p-value
Using the technology or normal distribution area tables, the p-value is,
p = 2P(z > 2.40)
= 2[1-P(z 2.40)]
= 2[2-0.9928]
= 2[0.0082] = 0.0164
The p-value < 0.05. Reject the null hypothesis.
There is no sufficient evidence to believe that, the proportion of airplance accidents due to pilot error is 0.5.

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