2. A researcher for the FAA wants to estimate the average flight time (in minute
ID: 3370210 • Letter: 2
Question
2. A researcher for the FAA wants to estimate the average flight time (in minutes) fronm Albuquerque, NM to Dallas, TX for flights with American Airlines. He randomly selects 9 flights and obtains x-103.4 minutes. With ?-8 minutes, can a 95% confidence interval be constructed? (Look at the normal plot and boxplot). If the conditions for a Z- interval are met, construct a 95% confidence interval. Since n is 30 or more we would say we conditions are not met. However, the raw data was analyzed and the following resulted: Probability Plot of Flight Times Boxpl ot of Flight Times 0 90 100) 110 20 30 140 5 100 110 125 120 Right Tmes Right Times From the first plot (the normal probability plot), if the data line closely to the line (are linear) and if you have results from MINITAB 18, 17 or 16 you will have the 95% confidence interval lines (if the date lie between those two curved lines) you can say that the data does not seem to deviate from normality. The boxplot further confirms this by showing there are not outliers. Therefore it is reasonable to assume our data is normally distributed- our sampling distribution is normally distributed. So it is reasonable to use the z procedures to determine a confidence interval. If conditions were not met you would not be able to answer a and b. a. Determine the 95% Confidence Interval b. If I wanted a margin of error no greater than 4.8 what sample size would I need for a 95% confidence interval?Explanation / Answer
a)
n = 9 , mean = 103.4 , s = 8
t value at 95% = 1.96
CI = mean +/- t * (s/sqrt(n))
= 103.4 +/- 1.96 * ( 8/sqrt(9))
= (98.1733,108.6267)
The 95% CI is (98.1733,108.6267)
b)
z value at 95% = 1.96, ME = 4.8 , s = 8
ME = z * (s/sqrt(n))
4.8 = 1.96 * (8/sqrt(n))
n = 11
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