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Statistical Inference and t-Tests

Objectives

? Evaluate the difference between a sample mean and a target value using a one-sample t-test. ? Evaluate the difference between a sample mean and a target value using a confidence interval. ? Assess the power of a hypothesis test using power analysis. ? Evaluate the difference between two sample means using a two-sample t-test. ? Evaluate the differences between paired observations using a paired t-test.

Statistical Inference and t-Tests

Copyright ? 2010 Minitab Inc. All rights reserved. Rel16 Ver 1.0

TRMEM160.SQBS

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Contents

Examples and Exercises Choosing an Analysis

Example 1 Mortgage Process Time

Exercise A Surgical Scheduling Time

Power and Sample Size Example 2 Evaluating Power

Two-Sample t-Test Example 3 Customer Complaints Exercise B Call Center Handling Times Exercise C Salary Comparison

Contents

Purpose

Evaluate the difference between mean mortgage processing time and a target value using a one-sample t-test. Evaluate the difference between mean surgical time and a target value using a one-sample t-test.

Assess the power of a hypothesis test.

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Evaluate the differences in the mean number of customer complaints using a two-sample t-test.

Compare the difference in call center handling times using a two-sample t-test.

Compare the difference in household salaries in two neighborhoods with a two-sample t-test.

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Statistical Inference and t-Tests

Copyright ? 2010 Minitab Inc. All rights reserved. Rel16 Ver 1.0

TRMEM160.SQBS

1-2

Examples and Exercises

Paired t-Test

Example 4 ATM Surrounds

Exercise D Car Satisfaction Ratings

Purpose

Evaluate the difference in ATM usage before and after installation of shelters Use a paired t-test to compare the difference in car satisfaction ratings one week and one year after customers purchase the car.

Contents Page

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Statistical Inference and t-Tests

Copyright ? 2010 Minitab Inc. All rights reserved. Rel16 Ver 1.0

TRMEM160.SQBS

1-3

Choosing an Analysis

Choosing an Analysis

Statistical Inference and t-Tests

Copyright ? 2010 Minitab Inc. All rights reserved. Rel16 Ver 1.0

TRMEM160.SQBS

1-4

One-Sample t-Test

Example 1 Mortgage Process Time

Problem

A faster loan processing time produces higher productivity and greater customer satisfaction. A financial services institution wants to establish a baseline for their process by estimating their mean processing time. They also want to determine if their mean time differs from a competitor's claim of 6 hours.

Data collection

A financial analyst randomly selects 6 loan applications from the past 2 weeks and manually calculates the time between loan initiation and when the customer receives the institution's decision.

One-Sample t-Test

Tools

? 1-Sample t ? Normality test ? Time series plot

Variable Date Hours

Description

Date of customer notification

Number of hours until customer receives notification

Statistical Inference and t-Tests

Copyright ? 2010 Minitab Inc. All rights reserved. Rel16 Ver 1.0

TRMEM160.SQBS

1-5

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