One-Sample t-test
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One-Sample t-test
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One-Sample t-test. What do these problems we have been working on have in common?. - PowerPoint PPT Presentation
Transcript of One-Sample t-test
One-Sample t-test
What do these problems we have been working on have in common?
In a population of American graduate students, individuals earn on average $7.25/hour on alcohol, with a standard deviation of $5. I jokingly ask whether or not graduate students from Brooklyn earn a different wage than grad students in general. I gather together 9 graduate students from this program and calculate the average amount they earn an hour: $11.00. Use an alpha level of .01.
How do I know I need to be using a z-test?
1. We are comparing a sample mean to a KNOWN population mean.
2. We KNOW the population .
What to do if you do not know the Population Standard Deviation ()?
Use the best estimate of x
You must correct for the uncertainty of this estimate.
Where s = s
x_
T-score for a single sample mean
What to do if you do not know the Population Standard Deviation ()?
x_
x_
Hypothesis testing with the t-statistic
Outcome “t”
Pro
bab
ilit
y
Retain H0 Reject H0
t-crit
One-tailed test
One-Sample t-testz-test is used when we know both and
t-test is when we know but not
The Sampling Distribution of the t-test
This table lists the critical value of the t-statistic for the Degrees of freedom and level.
Given the level and the df you can find the critical value of the t-statistic that divides the outcomes into reject or retain the null.
The average IQ score of Americans is 100. I believe that my Statistics class (you guys!) have different IQs than the general population. I force all 15 of you to take an IQ test, and I calculate a mean of 110 (s= 20). Use an alpha level of .05 to determine if this class has a different IQ than the population.
How do I know I need to be using a one-sample t-test?
Go to t-table! Must figure out of this is one- or two-tailed, and df.
Step 1: State the null and alternative hypotheses:
Step 2: Find the critical value.
H0: My stats class does not have a different IQ than the average AmericanH1: My stats class has a different IQ than the average American
The Sampling Distribution of the t-test
This table lists the critical value of the t-statistic for the Degrees of freedom and level.
Given the level and the df you can find the critical value of the t-statistic that divides the outcomes into reject or retain the null.
The average IQ score of Americans is 100. I believe that my Statistics class (you guys!) have different IQs than the general population. I force all 15 of you to take an IQ test, and I calculate a mean of 110 (s= 20). Use an alpha level of .05 to determine if this class has a different IQ than the population.
How do I know I need to be using a one-sample t-test?
Go to t-table! Must figure out of this is one- or two-tailed, and df.
Step 1: State the null and alternative hypotheses:
Step 2: Find the critical value.
H0: My stats class does not have a different IQ than the average AmericanH1: My stats class has a different IQ than the average American
+/-2.145
Step 3: Calculate the obtained statistic:
Step 4: Make a decision.
x
xobt s
xt
=
110 -100________
20/sqrt(15)= 1.93
Step 4: Retain the null hypothesis.-2.15
I2.15 I
The average IQ score of Americans is 100. I believe that my Statistics class (you guys!) have different IQs than the general population. I force all 15 of you to take an IQ test, and I calculate a mean of 110 (s= 20). Use an alpha level of .05 to determine if this class has a different IQ than the population.
= 10/5.17
The Sampling Distribution of the t-test
This table lists the critical value of the t-statistic for the Degrees of freedom and level.
Given the level and the df you can find the critical value of the t-statistic that divides the outcomes into reject or retain the null.
