Hypothesis Testing Section 8.1 - 8.2 Problem Statistics students believe that the mean score on the first statistics test is 65. A statistics instructor thinks the mean score is higher than 65. He samples ten statistics students and obtains the scores 65 65 70 67 66 63 63 68 72 71. He performs a hypothesis test using a 5% level of significance. The data are assumed to be from a normal distribution. a. Use your calculator to determine appropriate statistics for this problem. Go to "Stat" and "Edit" to input the data under list 1. Then, go to "Stat", "Calc", and "1-var stats". Click "enter". Find the sample mean, x, and the sample standard deviation, s. Write down these two values. Note that we are using the sample standard deviation in this problem since we are not told to use the population standard deviation. This typically happens when the sample size is small. mean, x: 67 standard deviation, s: 3.1972 b. State the null and alternate hypotheses. Remember, the null hypothesis involves the claimed population mean. The alternate hypothesis will use the same number as the null hypothesis but will use one of the following symbols: , or #. You will make your decision based on hints from the problem (or the sample mean you found from the calculation in part a). Ho=65 H1 >65 I C. What is alpha, the level of significance, from this problem? Write this value as a decimal. a=.05 d. Would you perform a one-tailed or two-tailed test? Why? What key words can you use from the problem to help you make this decision? This would be a one-tailed test with an unknown population standard deviation. e. If you are performing a one-tailed test, would it be a right or left-tailed test? How do you know? It would be a one-tailed and it would be to a right-tailed test f. What assumptions are necessary to perform this test