7. We are given a sample of size 25 from a very large population with a normal distribution, which yields a sample meanequal to 20 and asamplevariance equal to 100. Withmthe unknown population mean, using a 10% level of significance,test Ho:m>26vs H1:m

1. Set up the null and alternative hypotheses, clearly defining any unknown parameters. Ho always includes the "=" value and any other values for which you would take the same action as the "=" value. 2. Find a test statistics: (1) sensitive to the unknown parameter with (2) known distribution under the "=" value of the unknown parameter. Note we typically use a list of distribution facts to find a test statistic, substituting the "=" value of the unknown parameter under the null hypothesis to get the test statistic. Do NOT substitute for the estimate of the unknown parameter. State and label (a) the distribution fact and (b) the test statistic. 3. Look at the test statistic and alternative hypothesis and decide what values of the test statistics would tend to indicate that the alternative hypothesis is true (general direction). 4. Use the results of #2 and #3 along with the value of the probability of a type I error to find the cutoff point(s) for the acceptance and rejection region(s). Note a=Pr {Reject HolHo true} 5. Clearly state your decision rules. 6. Calculate your test statistic and using #, decide whether you will accept or reject the null hypo. Interpret your results