Inference for a Population Mean

1
Inference for a Population Mean

• Review

2
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.

3
Two types of inference

• Confidence Interval Used to estimate a
  population mean.
• Hypothesis test Used to test a claim about the
  population mean.

4
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

5
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.

6
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
  SUVs and highway gas mileage?

7
Correlation

• Both examples involve investigating correlation
  between a CATEGORICAL and a NUMERIC variable.
• Recall the appropriate test in this situation is
  ANOVA.

8
Section 7.3

• Understanding the Difference Between Sample
  Variability and Within Sample Variability
• Well use an example involving highway m.p.g. of
  various models of trucks to motivate this topic.