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**(Hypothesis test for small sample sizes)**

T-Test (Hypothesis test for small sample sizes)

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**Find the critical value for**

Left tail, n = 15

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**Find the critical value for**

Right tailed ; n = 10

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**Find the critical value for**

Two-tailed, n = 28

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**Assumptions: SRS (Simple Random Sample)**

The population is normally or approximately normally distributed Population Standard deviation is unknown and n < 30

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**The Standardized test statistic t is:**

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Example: The American Automobile Association claims that the mean nightly lodging rate for a family of four traveling on vacation in California is at least $136. A random sample of eleven such families has a mean nightly lodging rate of $126 with a standard deviation of $12. Is there enough evidence to reject the claim at Assume the population is normally distributed.

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**a) Write the null and alternative hypothesis mathematically and identify the claim**

: (claim) :

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**Find the critical values and identify the rejection region**

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**Find the standardized test statistic**

=

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Conclusion Decide whether to reject or fail to reject the null hypothesis. Then interpret the decision in the context of the original claim. At the 10% level, reject the null hypothesis. Evidence does not supports the claim that the mean daily meal cost is greater than or equal to $136.

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Now do Practice 7.3

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Section 7.2 Hypothesis Testing for the Mean (Large Samples) © 2012 Pearson Education, Inc. All rights reserved. 1 of 101.

Section 7.2 Hypothesis Testing for the Mean (Large Samples) © 2012 Pearson Education, Inc. All rights reserved. 1 of 101.

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