Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Transcript

T-Test (Hypothesis test for small sample sizes) Find the critical value for • Left tail, n = 15 0.05 t0 1.761 Find the critical value for • Right tailed ; n = 10 0.01 t0 2.821 Find the critical value for • Two-tailed, n = 28 0.02 t0 2.473 t0 2.473 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: x t s/ n 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 0.10 ? Assume the population is normally distributed. • a) Write the null and alternative hypothesis mathematically and identify the claim H0 Ha $136 : $136 : (claim) • Find the critical values and identify the rejection region 1.372 Find the standardized test statistic 126 136 t 12 / 11 = -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