Respuesta :
Answer:
d. less than the critical value, we can conclude that the proportion of United Airline flights that arrive on-time is less than 0.90
Step-by-step explanation:
Expedia would like to test the hypothesis that the proportion of Southwest Airline flights that arrive on-time is less than 0.90.
At the null hypothesis, we test that the proportion is of 0.9, that is:
[tex]H_0: p = 0.9[/tex]
At the alternate hypothesis, we test that it is less than 0.9, that is:
[tex]H_a: p < 0.9[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.9 is tested at the null hypothesis:
This means that [tex]\mu = 0.9, \sigma = \sqrt{0.9*0.1}[/tex]
A random sample of 140 United Airline flights found that 119 arrived on-time.
This means that [tex]n = 140, X = \frac{119}{140} = 0.85[/tex]
Value of the test-statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.85 - 0.9}{\frac{\sqrt{0.9*0.1}}{\sqrt{140}}}[/tex]
[tex]z = -1.97[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion of 0.85 or less, which is the p-value of z = -1.97.
Looking at the z-table, z = -1.97 has a p-value of 0.0244.
The p-value is 0.0244 < 0.05, which means that the test statistic is less than the critical value, and thus, we can conclude that the proportion of United Airline flights that arrive on-time is less than 0.90.
The correct answer is given by option d.
