Lab 10 Instructions and Questions for Excel 2007 Inferential Statistics and Hypothesis Testing NAME LAB TIME LAB BLDG This lab will carry out hypothesis tests and will examine the conditions which result in rejection of the null hypothesis 1 Go to the course webpage and open the lab10data file 2 Suppose we are interested in a variable whose mean is supposed to be 100 The distribution of this variable is believed to be normal with a standard deviation 0 8 mm based on previous surveys We want to detect a shift in the mean in either direction 3 The null hypothesis should be Ho 4 5 The alternate hypothesis should be Ha To examine the effect of sample size we will use two sample sizes n 30 and n 6 The first sample of 30 observations is given in column B and the first sample of 6 observations is given in Column K Use A45 through A49 for labels as follows A45 sample size A46 sample mean A47 test statistic z A48 1 side P Value A49 2 side P Value In B45 enter 30 for sample size In B46 use the AVERAGE function to calculate the sample mean for B10 B39 In B47 calculate the test statistic z using the formula z sample mean hypothesized mean 0 8 sqrt of sample size Enter B46 100 0 8 SQRT B45 In B48 use the NORMSDIST function to calculate the 1 side P Value Enter NORMSDIST B47 In B49 use the NORMSDIST function to calculate the 2 side P Value Enter 2 NORMSDIST B47 6 7 8 9 10 11 CALCULATE 7 NEW COLUMNS OF HYPOTHETICAL SAMPLES OF SIZE 30 12 In Column C generate a new sample of n 30 items using excel to deduct 0 1 from each data value in the column B ie in C10 use the formula B10 0 1 Copy this formula down to generate 30 new values 13 Repeat the above instructions to generate 6 new data samples in columns D through I except deduct 0 05 instead of 1 from the column on the left 14 Copy the formulas in B45 B49 across to column I 15 The sample means in line 46 should be 100 99 9 99 85 99 80 99 75 99 70 99 65 99 60 and the corresponding test statistics and P Values should be descending also CALCULATE 8 NEW COLUMNS OF HYPOTHETICAL SAMPLES OF SIZE 6 16 In Column K a sample of n 6 items is given In Column L generate a new sample of size n 6 using excel to deduct 0 15 from each data value in column K 17 Repeat the above instructions to generate 7 new samples in columns M through S except deduct 0 10 instead of 0 15 from the column on the left 18 In K45 enter 6 Copy K45 across to columns L through S Copy the formulas in I46 I49 over to columns K through S 19 20 The sample means from K46 through S46 should be 100 99 85 99 75 99 65 99 15 There should be two graphs between lines 51 and 102 showing the sample means and the associated P Values which you just generated The second plot just expands the y axis of the first plot to aid in interpretation INTERPRETATION OF SAMPLES 1 8 WHEN SAMPLE SIZE 30 21 The first sample of n 30 in Column B has a mean 100 exactly as expected in the null hypothesis Samples 2 8 in Columns C through I have descending means Note that the P Values are also descending from Column B through I 22 Remember that you can reject the null hypothesis only when the P Value is equal to or less than the significance level 23 Sample 1 in Column B supports which hypothesis Null Alternate 24 As the sample mean decreases going from Column B toward Column I the null hypothesis becomes Easier to believe Harder to believe 25 If 10 and with a two side Ha rejection of the null hypothesis would begin with what sample mean 26 If 01 and with a two side Ha rejection of the null hypothesis would begin with what sample mean 27 If 10 and with a one side Ha rejection of the null hypothesis would begin with what sample mean 28 If 01 and with a one side Ha rejection of the null hypothesis would begin with what sample mean 29 In general is it easier more likely or harder less likely to reject a 2 side hypothesis than it is to reject a one side hypothesis COMPARISON OF SAMPLE SIZE N 30 WITH N 6 30 Comparing sample size n 30 with n 6 for a given value of the sample mean and for a given set of hypotheses the P Value is always lower for which sample size 31 For detecting small shifts in the population mean it would be better to use a large sample size or a small sample size COMPARISON OF 10 VS 01 32 In general which value of would result in rejection of Ho more often 10 or 01 33 Which value of would be regarded as the most rigorous criteria most difficult to achieve for rejection of Ho 10 or 01 34 The P Value represents the probability that the particular value of the sample mean or a value more extreme could occur by chance alone WHEN THE NULL HYPOTHESIS IS ACTUALLY TRUE Knowing this which value of would result is more cases where Ho is rejected when Ho is actually true ie the mean is actually 100 10 or 01 Print the spreadsheet including the plots of P Values A1 S104 using landscape with a page break after line 43 and turn in with your answers to the questions