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One-Sample t-test. What do these problems we have been working on have in common?. - PowerPoint PPT Presentation

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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?

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.

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