Question

The mean number of flight hours for Continental Airline pilots is 49 hours per month. Assume that this mean was based on a sample of 100 Continental pilots and that the sample standard deviation was 11.5 hours. (a) Calculate the margin of error for a 95% confidence interval. (b) Calculate the upper bound for a 95% confidence interval.

Answer 1

Answer with explanation:

(a)

Mean number of flight hours for Continental Airline pilots = 49 hours per month

Total Sample Size =100

Standard Deviation =11.5 Hours

Margin of error for a 95% confidence interval

        $=Z_{95 \text{Percent}}\times \frac{\sigma}{\sqrt{n}}\\\\=0.8365 \times \frac{11.5}{\sqrt{100}}\\\\=\frac{9.61975}{10}\\\\=0.961975\\\\=0.97(\text{Approx})$

(b)

The Range of values for a 95% confidence interval

 ⇒     Mean number of flight  + Margin of Error  ≤  Confidence interval ≤    Mean number of flight  - Margin of Error      

⇒ 49+0.97  ≤  Confidence interval ≤ 49-0.97

⇒ 49.97  ≤  Confidence interval ≤48.03

Upper Bound = 49.97