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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 = -2.76

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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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