Question

Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to determine of the mean number of unoccupied seats on all its flights is greater than 10. To accomplish this, the records of 60 flights are randomly selected and the number of unoccupied seats is noted for each of the sampled flights. The sample mean is 11.4 seats and the sample standard deviation is 3.4 seats. Test the claim that mean number of unoccupied seats on all its flights is greater than 10 at the 5% significance level.

Answer 1

: Mean number of unoccupied seats

Claim : mean number of unoccupied seats on all its flights is greater than 10 : >10

Null hypothesis : Ho: =10

Alternative hypothesis : H1: > 10

Right tailed test.

Given,

Number of flights randomly selected : sample size : n= 60

Sample mean number of of unoccupied seats: = 11.4

Sample standard deviation :s = 3.4

hypothesized mean : =10

For right tailed test :

Degrees of freedom = n-1 =60-1=59

For 59 degrees of freedom, P(t>3.1898) =0.0011

p-value = P(t>3.1898) =0.0011

significance level = 5% ; =0.05

As p-value i.e. is less than Level of significance i.e (P-value:0.0011 < 0.05:Level of significance); Reject the Null Hypothesis
There is sufficient evidence to conclude that the mean number of unoccupied seats on all its flights is greater than 10