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# Hypothesis Testing

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by

Tweet## Emre Erdogan

on 24 December 2012#### Transcript of Hypothesis Testing

Remember the Research Cycle Hypothesis Testing Logic of Hypothesis Testing Steps in Hypothesis Testing 1. Making Assumptions

random sample

interval/rato

N > 50 Mean earnings of black americans is 24100 USD, population mean is 28895 USD, is this difference by chance or not? the Research and Null Hypothesis Research Hypothesis: A statement reflecting the substantive hypothesis. It is always expressed in terms of population parameters, but its specific form varies from test to test.

Null Hypothesis: A statement of "no difference" that contradicts the research hypothesis and is always expressed in terms of population parameters.

Alternative Hypothesis: a hypothesis that

contradicts the null hypothesis. E.g., the parameter

does not equal zero. One tailed test: a type of hypothesis test that involves a directional hypothesis.

Right/Left tailed test: a one tailed test in which the sample outcome is hypothesized to be at the right/left tail of the sampling distribution

Two tailed test: a type of hypothesis test that involves a nondirectional research hypothesis. Probability Values and Alpha P Values: the probability associated with the obtained value of Z.

Z-Value: the test statistic computed by converting a sample statistic to a Z score.

Alpha: the level of probability at which the null hypothesis is rejected.

Type 1 Error: the probability associated with rejectig a null hypothesis when it is TRUE

Type 2 Error: the probability associated with failing to reject a null hypothesis when it is FALSE 2. Stating the Research and Null Hypotheses 3. Decide on the Confidence Level and Alpha

Confidence Level=95%

Alpha= 5%

Z Criticial= 1.96 <= One Tailed 4. Selecting the sampling distribution and specify the test statistic:

n=100,

mean=24,100 USD,

pop. std. deviation= 23,3351

z test 5. Compute test statistic: 6. Making a decision and interpreting the results: 1. Making Assumptions

random sample

interval/rato

N > 50 2. Stating the Research and Null Hypotheses 3. Decide on the Confidence Level and Alpha

Confidence Level=90%

Alpha= 10%

Z Criticial= 1.28 <= One Tailed 4. Selecting the sampling distribution and specify the test statistic:

n=1143,

mean=6.2

pop. std. dev.= 2.42

z test 5. Compute test statistic: 6. Making a decision and interpreting the results: At a confidence level of 90 percent, I reject the null hypothesis that Turkish voters' average positioning in the left right spectrum is lower than or equal to the world average. Population Variance is not known 1. Making Assumptions

random sample

interval/rato

N > 50 2. Stating the Research and Null Hypotheses 3. Decide on the Confidence Level and Alpha

Confidence Level=90%

Alpha= 10%

t Criticial= 1.65 <= One Tailed 4. Selecting the sampling distribution and specify the test statistic:

n=1143,

mean=6.2

std. dev.= 2.42

t test, d.f.=1142 5. Compute test statistic: 6. Making a decision and interpreting the results: At a confidence level of 90 percent, I reject the null hypothesis that Turkish voters' average positioning in the left right spectrum is lower than or equal to the world average. Hypothesis Testing with Proportions 1. Making Assumptions

random sample

proportions 2. Stating the Research and Null Hypotheses 3. Decide on the Confidence Level and Alpha

Confidence Level=95%

Alpha= 5%

Z Criticial= 1.65 <= One Tailed 4. Selecting the sampling distribution and specify the test statistic:

n=1024,

p=0.54

Z test 5. Compute test statistic: 6. Making a decision and interpreting the results: At a confidence level of 95 percent, I reject the null hypothesis that percentage of "Yes" votes is less than or equal to 50.1 percent. Last survey showed that percentage of those approving the full membership of Turkey to the EU is 54 %. (n=1024) Difference of Means Test 1. Making Assumptions

random sample

difference of means 2. Stating the Research and Null Hypotheses 3. Decide on the Confidence Level and Alpha

Confidence Level=95%

Alpha= 5%

Z Criticial= 1.65 <= One Tailed 4. Selecting the sampling distribution and specify the test statistic: 5. Compute test statistic: 6. Making a decision and interpreting the results: Difference of Proportions 1. Making Assumptions

random sample

difference of proportions 2. Stating the Research and Null Hypotheses 3. Decide on the Confidence Level and Alpha

Confidence Level=95%

Alpha= 5%

Z Criticial= 1.65 <= One Tailed 4. Selecting the sampling distribution and specify the test statistic: 5. Compute test statistic: 6. Making a decision and interpreting the results:

Full transcriptrandom sample

interval/rato

N > 50 Mean earnings of black americans is 24100 USD, population mean is 28895 USD, is this difference by chance or not? the Research and Null Hypothesis Research Hypothesis: A statement reflecting the substantive hypothesis. It is always expressed in terms of population parameters, but its specific form varies from test to test.

Null Hypothesis: A statement of "no difference" that contradicts the research hypothesis and is always expressed in terms of population parameters.

Alternative Hypothesis: a hypothesis that

contradicts the null hypothesis. E.g., the parameter

does not equal zero. One tailed test: a type of hypothesis test that involves a directional hypothesis.

Right/Left tailed test: a one tailed test in which the sample outcome is hypothesized to be at the right/left tail of the sampling distribution

Two tailed test: a type of hypothesis test that involves a nondirectional research hypothesis. Probability Values and Alpha P Values: the probability associated with the obtained value of Z.

Z-Value: the test statistic computed by converting a sample statistic to a Z score.

Alpha: the level of probability at which the null hypothesis is rejected.

Type 1 Error: the probability associated with rejectig a null hypothesis when it is TRUE

Type 2 Error: the probability associated with failing to reject a null hypothesis when it is FALSE 2. Stating the Research and Null Hypotheses 3. Decide on the Confidence Level and Alpha

Confidence Level=95%

Alpha= 5%

Z Criticial= 1.96 <= One Tailed 4. Selecting the sampling distribution and specify the test statistic:

n=100,

mean=24,100 USD,

pop. std. deviation= 23,3351

z test 5. Compute test statistic: 6. Making a decision and interpreting the results: 1. Making Assumptions

random sample

interval/rato

N > 50 2. Stating the Research and Null Hypotheses 3. Decide on the Confidence Level and Alpha

Confidence Level=90%

Alpha= 10%

Z Criticial= 1.28 <= One Tailed 4. Selecting the sampling distribution and specify the test statistic:

n=1143,

mean=6.2

pop. std. dev.= 2.42

z test 5. Compute test statistic: 6. Making a decision and interpreting the results: At a confidence level of 90 percent, I reject the null hypothesis that Turkish voters' average positioning in the left right spectrum is lower than or equal to the world average. Population Variance is not known 1. Making Assumptions

random sample

interval/rato

N > 50 2. Stating the Research and Null Hypotheses 3. Decide on the Confidence Level and Alpha

Confidence Level=90%

Alpha= 10%

t Criticial= 1.65 <= One Tailed 4. Selecting the sampling distribution and specify the test statistic:

n=1143,

mean=6.2

std. dev.= 2.42

t test, d.f.=1142 5. Compute test statistic: 6. Making a decision and interpreting the results: At a confidence level of 90 percent, I reject the null hypothesis that Turkish voters' average positioning in the left right spectrum is lower than or equal to the world average. Hypothesis Testing with Proportions 1. Making Assumptions

random sample

proportions 2. Stating the Research and Null Hypotheses 3. Decide on the Confidence Level and Alpha

Confidence Level=95%

Alpha= 5%

Z Criticial= 1.65 <= One Tailed 4. Selecting the sampling distribution and specify the test statistic:

n=1024,

p=0.54

Z test 5. Compute test statistic: 6. Making a decision and interpreting the results: At a confidence level of 95 percent, I reject the null hypothesis that percentage of "Yes" votes is less than or equal to 50.1 percent. Last survey showed that percentage of those approving the full membership of Turkey to the EU is 54 %. (n=1024) Difference of Means Test 1. Making Assumptions

random sample

difference of means 2. Stating the Research and Null Hypotheses 3. Decide on the Confidence Level and Alpha

Confidence Level=95%

Alpha= 5%

Z Criticial= 1.65 <= One Tailed 4. Selecting the sampling distribution and specify the test statistic: 5. Compute test statistic: 6. Making a decision and interpreting the results: Difference of Proportions 1. Making Assumptions

random sample

difference of proportions 2. Stating the Research and Null Hypotheses 3. Decide on the Confidence Level and Alpha

Confidence Level=95%

Alpha= 5%

Z Criticial= 1.65 <= One Tailed 4. Selecting the sampling distribution and specify the test statistic: 5. Compute test statistic: 6. Making a decision and interpreting the results: