_{Up Learn – A Level maths (edexcel) – Testing a Population Mean}

_{Up Learn – A Level maths (edexcel) – Testing a Population Mean}

**Hypothesis Testing: Normal Distribution**

**Hypothesis Testing: Normal Distribution**

**Here’s a summary of everything you need to know about hypothesis testing for normal distributions at A Level.**

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### More videos on Testing a Population Mean:

^{Introduction to Testing a Population Mean (free trial)}

^{Sample Means and Population Means (free trial)}

^{How Sample Size Affects Sample Means (free trial)}

^{Probabilities of Sample Means (free trial)}

^{Modelling the Sample Mean (free trial)}

^{The Standard Deviation of the Sample Mean’s Distribution (free trial)}

^{When Should We Question Our Population Mean? (free trial)}

^{Finding Critical Regions and Critical Values (free trial)}

^{What Are the Hypotheses? (free trial)}

^{Performing a One-Tailed Test for a Population Mean (free trial)}

^{Performing a Two-Tailed Test for a Population Mean (free trial)}

^{Testing a Population Mean with the Standard Normal Distribution (free trial)}

## Hypothesis Tests

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2. Statistics vs Parameters

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3. The World is Unknowable

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4. Don’t Treat Parameter Estimates as Final

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5. Population Proportions

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6. When Should We Question Our Parameter Estimates?

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7. Critical Regions

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8. Critical Regions With Two Tails

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9. One or Two Tails?

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10. Critical Values

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11. Acceptance Region

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12. Type 2 Errors

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13. Type 1 Errors

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14. Remembering Which is Which

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15. Significance

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16. Significance Levels

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17. Significance Levels with Two Tails

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18. Actual Significance Levels

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19. Common Significance Levels

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20. Two Ways of Setting a Significance Level

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21. Finding Critical Regions

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22. The Term ‘Hypothesis Testing’

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23. Population Parameters and Test Statistics

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24. What are Hypotheses?

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25. Null and Alternative Hypotheses

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26. Statistical Hypothesis Testing

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27. One-Tailed Tests and Two-Tailed Tests

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28. Representing the Null and Alternative Hypotheses

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29. Performing a One-Tailed Test

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30. A Second Way of Performing a One-Tailed Test

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31. Performing a Two-Tailed Test

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32. The Miraculous Dead Salmon

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2. Sample Means and Population Means

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3. How Sample Size Affects Sample Means

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4. Probabilities of Sample Means

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5. Modelling the Sample Mean

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6. The Standard Deviation of the Sample Mean’s Distribution

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7. When Should We Question Our Population Mean?

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8. Finding Critical Regions and Critical Values

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9. What Are the Hypotheses?

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10. Performing a One-Tailed Test for a Population Mean

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11. Performing a Two-Tailed Test for a Population Mean

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12. Testing a Population Mean with the Standard Normal Distribution

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13. Coding the Sample Means

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14. Hypothesis Testing With a Coded Sample Mean

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2. Correlation Coefficients from Samples and Populations

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3. Probabilities of Sample Correlation Coefficients

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4. Sample Size Matters

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5. Testing for Zero Correlation

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6. The Null and Alternative Hypotheses in PMCC Testing

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7. The Percentage Points Table

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8. Performing a One-Tailed Test for a Population PMCC

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9. Performing a Two-Tailed Test for a Population PMCC

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10. Where Were All the Distributions?

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11. Are Older People All Liars?

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Here’s a reminder of the key points you should know about testing a population mean.

Population means and sample means are often different.

But the bigger the sample, the closer the sample mean is likely to be to the population mean.

If a population is modelled using a normal distribution…

It’s possible to model the probabilities of observing different sample means like this.

Where ‘X bar’ represents the sample mean and n is the sample size.

Then, the variance of the new distribution is this and the standard deviation is this.

If we have an estimate for a population mean, we can test it out using hypothesis testing.

The logic goes: if the estimate is correct, we’re very unlikely to observe some sample means.

So if we take a sample and do observe those unlikely means, we should reject the estimate we currently have.

To find critical regions on a normal distribution, use the inverse normal distribution function on your calculator.

The hypotheses look pretty much the same as when we test using a binomial distribution.

It’s just that, since we’re forming hypotheses about mean values now, we use.

Finally then, the exam may tell you a sample was taken, tell you the significance level and ask you to perform the rest of the hypothesis test.

Here’s what that looks like for a one-tailed test.

First, write down the null and alternative hypotheses.

Second, write down the distribution for the sample mean.

Third, find and state the critical region.

Fourth, compare the test statistic to the critical region.

And fifth, write a conclusion.

An alternative method is to find the probability of observing the sample mean or anything greater,

Compare that to the significance level, and then write the conclusion accordingly.

The working looks very similar for a two-tailed test.

First, write down the null and alternative hypotheses.

Second, write down the distribution for the sample mean.

Third, find and state the critical region, now with two tails.

Fourth, compare the test statistic to the critical region.

And fifth, write a conclusion.

In place of this step, you could find the probability of observing the sample mean or anything greater,

Compare that to half of the significance level, since this is a two-tailed test,

And then write the conclusion accordingly.

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