Researchers at Purdue University and Wichita State University found that airlines are doing a better job of getting passengers to their destinations on time. AirTran Airways and Southwest Airlines were among the leaders in on-time arrivals with both having 88% of their flights arriving on time. But for the 12% of flights that were delayed, how many minutes were these flights late? Sample data showing the number of minutes that delayed flights were late are provided in the Excel Online file below. Data are shown for both airlines. Construct a spreadsheet to answer the following questions. Open spreadsheet a. Formulate the hypotheses that can be used to test for a difference between the population mean minutes late for delayed flights by these two airlines. population mean minutes late for delayed AirTran flights population mean minutes late for delayed Southwest flights Но : - U2 Нi : и1 - M2 b. What is the sample mean number of minutes late for delayed flights for each of these two airlines? AirTran (to 2 decimals) Southwest (to 2 decimals) c. Using a .05 level of significance, what is the p-value and what is your conclusion? p-value is (to 4 decimals) We reject Ho. cannot D2 * T Test: Two-Sample Assuming Unequal Variances Н XLMiner Analysis ToolPak AirTran Southwest Parts b&c 76 36 T Test: Two-Sample Assuming Uneglual Variances Anova: Single Factor 13 106 4 83 50 76 36 Anova: Two-Factor With Replication 12 79 Mean 72.79166667 69.42105263 6. 108 37 Variance 1271.824275 481.9239766 Anova: Two-Factor Without Replication 56 33 Observations 24 19 8 70 61 Hypothesized Mean Difference Correlation 9. 92 82 df 38 10 56 52 t Stat 0.380776251 Covariance P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail 11 80 75 0.352744879 12 79 1.685954405 Descriptive Statistics 13 73 74 0.705489757 14 111 71 2.024394147 Exponential Smoothing 15 119 72 16 71 80 F-Test Two-Sample for Variances 17 81 38 18 81 57 Part d Fourier Analysis 19 112 99 Significance Level (Alpha) 0.05 20 112 110 Formula Histogram Linear Regression Can we reject the null hypothesis? (Enter "Can" or "Cannot") 21 97 64 #N/A Logistic Regression 22 106 23 5 Moving Average 24 97 25 34 Random Number Generation 26 72 27 Rank and Percentile 28 29 Sampling 30 31 t-Test: Paired Two Sample for Means 32 33 t-Test: Two-Sample Assuming Equal Variances 34 35 t-Test: Two-Sample Assuming Unequal Variances 36
Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.
Find B and C:
Note: The data on the excel in the yellow box is wrong.
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