Question

An airline claims that the proportion of no-shows for passengers who booked on its flights is less than 0.06. In a random sample of 380 reservations, 19 were no-shows. A hypothesis test is to be performed to test the airline's claim that the proportion of no-shows on its flights is less than 0.06. Calculate the test statistic associated with this sample. 1.124 -1.943 -0.821 0.222 -1.571

Answer 1

Answer: -0.821

Explanation:

The test statistic for population proportion (p) is given by :-

`z=\frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}`

Given : An airline claims that the proportion of no-shows for passengers who booked on its flights is less than 0.06.

Sample size = 380

The proportion that there were no-shows =
`(19)/(380)=0.05`

The test statistic for population proportion (p) is given by :-

`z=\frac{0.05-0.06}{\sqrt{(0.06(1-0.06))/(380)}}\\\\=0.8208281581\approx-0.821`

Hence, the test statistic associated with this sample = -0.821

Answer 2

Step 1:

In a sample of 380 randomly selected reservations, 19 were no-shows.

Step 2:

Proportion of no shows p<0.06.

Step 3:

Test Value

z(19/380)=0.05

Step 4:

Test statistics

a) 0.05-1.124=-1.074

b) 0.05-(-1.943) = 0.05+1.943=1.993

c)0.05-(-0.821)=0.05+0.821=0.871

d)0.05 - 0.222 = - 0.172

e)0.05 -(-1.571) = 0.05+1.571 = 1.621

The above data clearly mentions the test statistics associated with the given samples.