Question

Data on 72 randomly selected flights departing from the three major NYC airports in 2013.

Departure delays in minutes. Negative times represent early departures.

dep_delay
-4
-3
58
-5
-5
-4
-1
-1
-1
-3
-5
-7
-5
-4
-5
-8
-2
4
-1
0
11
-5
37
22
65
6
-1
19
16
-5
178
-3
-5
4
-1
4
15
-3
-7
-6
-7
-3
-5
51
-4
-6
-1
-7
-11
2
1
102
-7
36
11
1
-6
-7
-5
-3
9
115
58
-2
-6
8
-4
-7
2
-5
303
18

Q1. We want to estimate the proportion of flights that departed from the NYC airports in 2013 which are delayed. There are two ways we can do this. We can either obtain a point estimate or calculate an interval estimate. Provide estimates using both methods. Use a 99% confidence level. Show all working, define variables and state the distribution as needed.

Answer 1

point estimate=  x̅ = ΣX/n =    13.5775

----------------

Level of Significance ,    α =    0.01          
degree of freedom=   DF=n-1=   70          
't value='   tα/2=   2.648   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   46.8224/√71=   5.5568          
margin of error , E=t*SE =   2.6479   *   5.5568   =   14.7139
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    13.58   -   14.7139   =   -1.1364
Interval Upper Limit = x̅ + E =    13.58   -   14.7139   =   28.2913
99%   confidence interval is (   -1.14   < µ <   28.29   )