nstructure.com/courses/9584/quizzes/10213/take/questions/126258 -Pror. K.Vantsto
ID: 3074867 • Letter: N
Question
nstructure.com/courses/9584/quizzes/10213/take/questions/126258 -Pror. K.Vantsto est mate tne proport on or Tignts Trom Newark, NJ Orlando, FL that are delayed due to weather issues on Labor Day weekend in September. To do this she gathered a sample of 120 flights from Newark, NJ to Orlando, FL taken over the last 10 years and recorded 32 delayed flights due to weather. Find the 95% confidence interval, interpret the confidence interval, and decide if the 36% delayed flights reported by Kayak.com is consistent with the true proportion. What are the following values? ROUND ANY DECIMAL ANSWERS TO 3 DECIMAL PLACES. n 120 X32 p-| .2666 Confidence level .95 7586.jpg IMG. 7585 jpg IMG 7583jpg
Explanation / Answer
Step 1: Find /2
Level of Confidence = 95%
= 100% - (Level of Confidence) = 5%
/2 = 2.5% = 0.025
Step 2: Find z/2
Calculate z/2 by using standard normal distribution (normal population with mean () = 0 and standard deviation () = 1)
with /2 = 0.025 as right-tailed area and left-tailed area.
So z/2 = +- 1.9599
Step 3
Lower Bound = p - z/2•p(1 - p)/n = 0.2666 - (1.9599)(0.0404) = 0.187
Upper Bound = p + z/2•p(1 - p)/n = 0.2666 + (1.9599)(0.0404) = 0.346
Confidence Interval = (0.187, 0.346)
0.2666 +- 0.0792
0.187 < p < 0.346
We are 95% confident that the interval from 0.187 to 0.346 contain true value of population proportion(p). 36% means 0.36 does not lie in this interval So not consistent.
MARGIN OF ERROR
The Margin of Error (MOE) is calculated according to the formula: MOE = z * p * (1 - p) / n
Where: z = 1.96 for a confidence level () of 95%, p = proportion (expressed as a decimal), n = sample size.
z = 1.96, p = 0.2667, n = 120
MOE = 1.96 * 0.2667 * (1 - 0.2667) / 120
MOE = 0.867 / 10.954 * 100 = 7.913%
The margin of error is ±7.913%
Best point estimate 0.2739
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