inference for the mean of a population section 11.1 ap exam registration deadline: march 17 th late...
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Inference for the Mean of a PopulationSection 11.1
AP Exam Registration Deadline: March 17th
Late Fee ($50): March 18th – March 24th
Financial Aid Application Due: TODAY!!!!!!
Get out homework!
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Conditions for Inference about a Mean
SRS of size n from the population of interest
Observations must be independent
Observations must have a normal distribution with mean µ and standard deviation σ
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What if σ isn’t given? Because σ is usually unknown, we
estimate it by the sample deviation s.
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Standard Error The standard error of the sample mean is
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When we know the value σ, we base confidence intervals and tests for µ on the z - statistic:
The z – statistic has a normal distribution.
When we do not know σ, we substitute the standard error . This statistic does not have a normal distribution…
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The t distributionDraw an SRS of size n from a population that has the normal distribution with mean µ and standard deviation σ. The one-sample t statistic
has the t distribution with n – 1 degrees of freedom.
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Different t distributions? There is a different t distribution for
each sample size.
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So how do we determine which one we use?
Degrees of freedom
n -1 , where n is the sample size.
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Example 11.1, p. 619Using the “t Table”
What critical value t* from Table C (t Table) would you use for a t distribution with 18 degrees of freedom having probability 0.90 to the left of t*?
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Example 11.1, p. 619Using the “t Table”
What critical value t* from Table C (t Table) would you use for a t distribution with 18 degrees of freedom having probability 0.90 to the left of t*?
Before we start, we will need the tail probability.
.90 probability
Tail area = .10
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Df = 18, Tail Area = .10
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Example 11.1, p. 619Using the “t Table”
What critical value t* from Table C (t Table) would you use for a t distribution with 18 degrees of freedom having probability 0.90 to the left of t*?
So the desired critical value is t* = 1.330.
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Example 11.1, p. 619Using the “t Table”
Now suppose you want to construct a 95% confidence interval for the mean µ of a population based on an SRS of size n = 12. What critical value of t* should you use?
Df = 12 – 1 = 11
Tail Area?
We don’t need it…look at the bottom of the chart.
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Example 11.1, p. 619Using the “t Table”
Now suppose you want to construct a 95% confidence interval for the mean µ of a population based on an SRS of size n = 12. What critical value of t* should you use?
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Example 11.1, p. 619Using the “t Table”
Now suppose you want to construct a 95% confidence interval for the mean µ of a population based on an SRS of size n = 12. What critical value of t* should you use?
So the desired critical value is t* = 2.201.
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Homework: P. 619: 11.1 a, 11.2, 11.4
Due: Tuesday
FYI: I have a meeting Friday morning, 3/8. I will have to cancel tutoring that day.