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Statistical Inference and t-Tests - Minitab

1. 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 1-1. Contents Contents Examples and Exercises Purpose Page Choosing an Analysis Example 1 Evaluate the difference between mean mortgage 1-5.

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Transcription of Statistical Inference and t-Tests - Minitab

1 1. 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 1-1. Contents Contents Examples and Exercises Purpose Page Choosing an Analysis Example 1 Evaluate the difference between mean mortgage 1-5.

2 Mortgage Process Time processing time and a target value using a one-sample t-test. Exercise A Evaluate the difference between mean surgical time and 1-19. Surgical Scheduling Time a target value using a one-sample t-test. Power and Sample Size Example 2 Assess the power of a hypothesis test. 1-20. Evaluating Power Two-Sample t-Test Example 3 Evaluate the differences in the mean number of customer 1-29. Customer Complaints complaints using a two-sample t-test. Exercise B Compare the difference in call center handling times 1-41. Call Center Handling Times using a two-sample t-test.

3 Exercise C Compare the difference in household salaries in two 1-42. Salary Comparison neighborhoods with a two-sample t-test. Statistical Inference and t-Tests Copyright 2010 Minitab Inc. All rights reserved. Rel16 Ver 1-2. Contents Examples and Exercises Purpose Page Paired t-Test Example 4 Evaluate the difference in ATM usage before and after 1-43. ATM Surrounds installation of shelters Exercise D Use a paired t-test to compare the difference in car 1-49. Car Satisfaction Ratings satisfaction ratings one week and one year after customers purchase the car.

4 Statistical Inference and t-Tests Copyright 2010 Minitab Inc. All rights reserved. Rel16 Ver 1-3. Choosing an Analysis Choosing an Analysis Statistical Inference and t-Tests Copyright 2010 Minitab Inc. All rights reserved. Rel16 Ver 1-4. One-Sample t-Test One-Sample t-Test Example 1 Mortgage Process Time Problem Tools A faster loan processing time produces higher productivity 1-Sample t and greater customer satisfaction. A financial services Normality test institution wants to establish a baseline for their process by Time series plot estimating their mean processing time.

5 They also want to determine if their mean time differs from a competitor's claim of 6 hours. Variable Description Data collection Date Date of customer notification A financial analyst randomly selects 6 loan applications from Hours Number of hours until customer receives the past 2 weeks and manually calculates the time between notification loan initiation and when the customer receives the institution's decision. Statistical Inference and t-Tests Copyright 2010 Minitab Inc. All rights reserved. Rel16 Ver 1-5. One-Sample t-Test Hypothesis testing What is a hypothesis test Why use a hypothesis test A hypothesis test uses sample data to test a hypothesis about Hypothesis testing can help answer questions such as: the population from which the sample was taken.

6 The Are turn-around times meeting or exceeding customer one-sample t-test is one of many procedures available for expectations? hypothesis testing in Minitab . Is the service at one branch better than the service at For example, to test whether the mean duration of a another? transaction is equal to the desired target, measure the duration of a sample of transactions and use its sample mean For example, to estimate the mean for all transactions. This is an example On average, is a call center meeting the target time to of Statistical Inference , which is using information about a answer customer questions?

7 Sample to make an Inference about a population. Is the mean billing cycle time shorter at the branch with a new billing process? When to use a hypothesis test Use a hypothesis test to make inferences about one or more populations when sample data are available. Statistical Inference and t-Tests Copyright 2010 Minitab Inc. All rights reserved. Rel16 Ver 1-6. One-Sample t-Test One-sample t-test What is a one-sample t-test Why use a one-sample t-test A one-sample t-test helps determine whether (the A one-sample t-test can help answer questions such as: population mean) is equal to a hypothesized value (the test Is the mean transaction time on target?)

8 Mean). Does customer service meet expectations? The test uses the standard deviation of the sample to estimate (the population standard deviation). If the difference For example, between the sample mean and the test mean is large relative On average, is a call center meeting the target time to to the variability of the sample mean, then is unlikely to be answer customer questions? equal to the test mean. Is the billing cycle time for a new process shorter than the current cycle time of 20 days? When to use a one-sample t-test Use a one-sample t-test when continuous data are available from a single random sample.

9 The test assumes the population is normally distributed. However, it is fairly robust to violations of this assumption for sample sizes equal to or greater than 30, provided the observations are collected randomly and the data are continuous, unimodal, and reasonably symmetric (see [1]). Statistical Inference and t-Tests Copyright 2010 Minitab Inc. All rights reserved. Rel16 Ver 1-7. One-Sample t-Test Testing the null hypothesis The company wants to determine whether the mean time for 1-Sample t the approval process is statistically different from the 1 Choose Stat Basic Statistics 1-Sample t.

10 Competitor's claim of 6 hours. In Statistical terms, the process mean is the population mean, or (mu). 2 Complete the dialog box as shown below. Statistical hypotheses Either is equal to 6 hours or it is not. You can state these alternatives with two hypotheses: The null hypothesis (H0): is equal to 6 hours. The alternative hypothesis (H1): is not equal to 6 hours. Because the analysts will not measure every loan request in the population, they will not know the true value of . However, an appropriate hypothesis test can help them make an informed decision.


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