Question

6. The mean number of hours of flying time for pilots at Continental Airlines is 37 hours per month (The Wall Street Journal, February 25, 2003). Assume that this mean was based on actual flying times for a sample of 49 Continental pilots and that the sample standard deviation was 8.2 hours. 6a. At 95% confidence, what is the margin of error? Solution 5b. What is the 95% confidence interval estimate of the UB

Answer 1

The marginal error is 2.355

Confidence interval is
`(34.645,\ 39.355)`

The LB and UB are 34.645 and 39.3555 respectively.

Explanation:

Consider the provided information.

n = 49, s = 8.2 c = 95%and
`\bar x=37`

Degree of freedom is: n-1 = 49-1 = 48.

`\alpha =(1-c)/(2)= (1-0.95)/(2)\\\alpha = (0.05)/(2)= 0.025`

From the table
`t_(\alpha /2)=2.010635`

Marginal error is:

`E=t_(\alpha /2)* (s)/(√(n))`

`E=2.0106* (8.2)/(√(49))`

`E=2.0106* (8.2)/(7)`

`E=2.0106* 1.171`

`E=2.355`

Hence, the marginal error is 2.355.

Part (B)

95% confidence interval estimate

`(\bar x-E,\ \bar x+E)`

`(37-2.355,\ 37+2.355)`

`(34.645,\ 39.355)`

Thus, the LB and UB are 34.645 and 39.3555 respectively.