Inference for a Population Mean

Review

How do sample means vary?

• According to a bell curve

• The average of the sample means is the population mean

• The standard deviation is the population standard deviation divided by the square root of the sample size.

Two types of inference

• Confidence Interval – Used to estimate a population mean.

• Hypothesis test – Used to test a claim about the population mean.

Confidence Interval Formula to Estimate a Population Mean

• If the population standard deviation is known or the sample size is large:

• If the population standard deviation is not known and the sample size is less than 30

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stx *

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Hypothesis Test to Test a Population Mean

• Null Hypothesis:

• Collect a random sample and compute a sample mean and standard deviation.

• Compute the t-test statistic

• Find the p-value

• State your conclusions.

00 : H

Looking Ahead

• Is there any association between gender and the amount of time one exercises per week?

• Is there any association between the model of SUV’s and highway gas mileage?

Correlation

• Both examples involve investigating correlation between a CATEGORICAL and a NUMERIC variable.

• Recall the appropriate test in this situation is ANOVA.

Section 7.3

• Understanding the Difference Between Sample Variability and Within Sample Variability

• We’ll use an example involving highway m.p.g. of various models of trucks to motivate this topic.