Statistical Inference Unit Application

Application Overview

Goals

Review the requirements for completing the Graded Assignment

Sharing Your Results

There are many possible reasons flight departures are delayed, including bad weather, delays of incoming flights, maintenance issues, and security concerns.

During this unit, you will construct a confidence interval to estimate the difference in mean delay times of two groups of flights, and another confidence interval to estimate the difference in the proportion of delayed flights for those two groups of flights.

In the first lesson, you will use a table of random digits to simulate choosing two simple random samples. In later assignments, you will use statistics from those samples to construct the confidence intervals.

Schedule of Completion

Part 1: Submit to your teacher via the Dropbox when you complete the Introduction to Unit 6.

Part 2: Submit to your teacher via the Dropbox when you complete the Mean Differences lesson.

Discussion: After you’ve completed Part 2 and if directed by your teacher, participate in a discussion with fellow students.

Part 3: Submit to your teacher via the Dropbox when you complete the Proportion Differences lesson.

Discussion: After your teacher has reviewed your work and if directed by your teacher, participate in a discussion with fellow students.

Graded Assignments for Statistical Inference

You will take two simple random samples, each from a different population, and use information from the samples to draw conclusions about how the populations compare.

Part 1 [After Lesson 6.1: Introduction]

Open Flight_Data.xls. The Jan_2011 tab lists all the Alaska Airlines departures from the Ted Stevens Anchorage International airport in January 2011. The June_2011 tab lists all the Alaska Airlines departures from the same airport in June 2011. In both, the departure delays times are shaded, simulating unknown values.
Use the Table of Random Digits on pages A3–A4 of your reference guide to select a simple random sample of 40 flights from the January 2011 group. Label the flights with the spreadsheet's row number; for example, each sample flight should be labeled with a number from 0009 to 1134. Enter the numbers in the Worksheet.doc file as you find them. Repeat for the June 2011 data, labeling each flight with a number from 0009 to 1512. On the worksheet, enter the line number you started at for each sample. Use a different starting point for each.
In the Flight_Data.xls sheet, select a departure delay cell for a flight in a sample. Change the cell's fill color to either none or a lighter color that lets you read the cell value. Enter the value in the appropriate row in the Worksheet.doc file. Repeat for the other flights in your samples. You can use F4 to repeat the last command. (Note: Positive numbers indicate delays; negative numbers indicate early departures.)
Find the mean and standard deviation of the departure delay times for each sample. Record the sample statistics in the worksheet. Use your graphing calculator, Excel, or GeoGebra to help determine these sample statistics.
Submit the Worksheet.doc file to your teacher with Part 1 completed for review.

This part of the assignment will be graded on the following criteria:

Simple random samples are collected, and means and standard deviations for each sample are calculated and recorded in the worksheet. (4 points)

Part 2 [After Lesson 6.4: Mean Differences]

Use the sample statistics you found in Part 1 to find and interpret a 95% confidence interval for the difference of the mean departure delay times of all the Alaska Airlines flights during January 2011 and June 2011. Complete Page 3 of the Worksheet.doc file to do this. While you may use technology to confirm your answer, you must fully show each step:

Margin of error: Show the formula with the critical z-score and standard deviation of the sampling distribution of the mean differences.
Confidence interval: Show the difference of the sample means, and how it is used with the margin of error.
Interpretation: Use complete sentences.

Submit the Worksheet.doc file to your teacher for review.

This part of the assignment will be graded on the following criteria:

Sample statistics have been used to correctly construct and report a 95% confidence interval for mean differences in delay times. (4 points)

Part 3 [After Lesson 6.6: Proportion Differences]

Use the sample data on Pages 1 and 2 in the Worksheet.doc file to determine the proportion of times a flight in each sample was delayed. Remember, delay times are positive. Record the sample proportions on Page 4.
Use the sample statistics to find and interpret a 95% confidence interval for the difference in the proportion of delayed flights for all the Alaska Airlines flights during January 2011 and June 2011. Complete Page 4 of the Worksheet.doc file to do this. While you may use technology to confirm your answer, you must fully show each step:

Margin of error: Show the formula with the critical z-score and standard deviation of the sampling distribution of the proportion differences.
Confidence interval: Show the difference of the sample proportions, and how it is used with the margin of error.
Interpretation: Use complete sentences.

Submit the Worksheet.doc file to your teacher for review.

This part of the assignment will be graded on the following criteria:

Sample statistics have been used to correctly construct and report a 95% confidence interval for differences in percent of delayed flights. (4 points)

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