(Hypothesis test for small sample sizes) T-Test (Hypothesis test for small sample sizes)

Find the critical value for Left tail, n = 15

Find the critical value for Right tailed ; n = 10

Find the critical value for Two-tailed, n = 28

Assumptions: SRS (Simple Random Sample)  The population is normally or approximately normally distributed Population Standard deviation is unknown and n < 30

The Standardized test statistic t is:

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.

a)      Write the null and alternative hypothesis mathematically and identify the claim : (claim) :

Find the critical values and identify the rejection region

Find the standardized test statistic = -2.76

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.

Now do Practice 7.3