River Station Length Weight Mercury 1 1 47 1616 1.6 1 1 48.7 1862 1.5 1 1 55.7 2855 1.7 1 1 45.2 1199 0.73 1 1 43.8 1225 0.51 1 1 38.5 870 0.48 1 1 45.8 1455 0.95 1 1 44 1220 1.4 1 2 47.7 3378 0.8 1 2 45.1 2920 0.34 1 2 43.5 2674 0.54 1 2 41 1904 0.9 1 2 33.7 1080 0.48 1 2 33.5 1146 0.57 1 2 32 894 0.61 1 2 29.5 754 0.38 1 2 34.9 1174 0.61 1 2 47.1 1435 1.5 1 2 44.2 1378 0.72 1 2 41 1059 1.8 1 2 41.6 873 1.6 1 2 39 857 0.98 1 2 38 743 0.88 1 2 36.1 622 1.5 1 2 33.4 503 0.73 1 3 32.8 406 1.2 1 3 31.4 362 1.1 1 3 33.6 360 1.6 1 3 29.5 313 0.87 1 3 30.5 314 0.9 1 3 30 336 0.61 1 3 33.5 448 0.99 1 3 31 263 0.2 1 3 65 4511 2.1 1 4 36 600 1.5 1 4 44 1132 0.2 1 4 40 898 1.2 1 4 44.5 1301 1.6 1 4 50.5 2021 1.2 1 4 50 1883 1.2 1 4 47 1546 1.2 1 5 26 234 0.28 1 5 30 323 0.51 1 5 30 430 0.27 1 5 29 353 0.35 1 5 31 402 0.57 1 5 41 1042 0.66 1 5 36.5 723 0.49 1 5 38 709 0.51 1 5 44 1455 0.73 1 5 39 879 1.4 1 5 48 1396 2.7 1 5 51.5 2369 0.8

1 5 56 3421 3.1 1 6 30.5 400 0.5 1 6 34 678 0.55 1 6 44.5 1853 2.7 2 7 35 620 0.73 2 8 30.4 320 0.51 2 8 36 574 1.6 2 8 34.7 491 0.58 2 8 31.7 407 0.5 2 8 34.5 496 0.58 2 8 40.1 805 1.4 2 9 33 518 0.55 2 9 40.5 970 0.84 2 9 37 673 0.76 2 9 35.5 550 0.65 2 9 40 856 1.1 2 9 35 487 1 2 9 39.5 923 1.2 2 9 31.5 521 0.74 2 9 30 348 0.41 2 9 33 440 0.78 2 9 47 586 1.3 2 9 54 2664 1.8 2 11 34.8 491 0.57 2 11 34.5 560 0.69 2 11 38.5 870 1.8 2 11 40 864 0.93 2 11 46.4 1285 0.1 2 12 41.9 1188 2.4 2 12 46.2 1365 0.88 2 12 47.3 1632 1.5 2 12 47.1 1725 1.8 2 12 56.5 2451 2.1 2 12 46.1 1327 0.91 2 12 28.5 303 0.61 2 12 36.5 566 0.1 2 12 46 1342 2.2 2 12 36.7 647 2.4 2 12 39 844 0.69 2 12 53 3026 2.7 2 12 36.5 656 0.65 2 12 41.5 1018 0.83 2 12 36.2 708 1.3 2 13 27.3 250 0.28 2 13 26.7 252 0.21 2 13 27.5 283 0.14 2 13 33.9 465 0.39 2 13 29.6 329 0.9 2 13 57.5 2401 1.4 2 13 49 1891 0.58 2 13 34.9 498 0.42 2 13 29 307 0.11 2 13 31.5 376 0.28 2 12 38.2 573 0.59

2 14 28.6 338 1.1 2 14 36.8 714 1.6 2 14 43.4 1251 1.3 2 15 50.8 2131 1.8 2 15 46.8 1604 1.8 2 15 40.2 1090 1.2 2 15 58.7 3315 2.9 2 15 56.1 2629 3.4 2 15 48 1743 1.9 2 15 44.7 1454 2.4 2 15 43.6 1245 1.8 2 15 37.6 937 2.4 2 15 40 869 1.4 2 15 46.5 772 1.7 2 15 36 724 1.3 2 16 50.4 1744 0.93 2 16 59.2 3524 3.6 2 16 49.5 1924 2.3 2 16 47.5 1546 1.4 2 16 54.2 3164 2.1 2 16 41.7 1255 1.4 2 16 36 702 0.92

State the test statistic and its sampling distribution (assume the standard deviations of the two populations are NOT the same the more conservative approach). Note: In this case, we would be testing to nd if there is a difference in means for the populaons, therefore, the null values #1 #2 or Md are equal to zero. A: t: (561 562) (M1 M2) 52 5% i + a B: (51 E2) (H1 H2) t: % W C: E Md I: 34 W Part IV. Two-sample Tests for Means Now suppose we want to compare the two rivers, and test the claim the fish have different mercury levels in the two rivers using a 0.01 level of significance. This might be helpful to know for health policy of the surrounding communities. First let's do a two-sample test by hand. To get the summary statistics, go to the JMP Starter window, Basic and select Distribution, and then in the dialog box put Mercury in "Y, Columns" and put River in the "By" box at the bottom, then click OK. .. . Distribution The distribution of values in each column Select Columns elected Columns into Roles Action 6 Columns Y, Columns Mercury OK River optional Station Cancel Length Weight Mercury Weight optional numeric Short Fish Remove Freq optional numeric Recall Histograms Only By River optional Help Your output window should have separate sections for each river. The display is easier to read if you choose the horizontal layout by clicking the red arrow next to Mercury. Select Display options and check the horizontal layout (do this for each River heading)Question 12 1 pts What is the value of the test statistic (t Ratio) computed by JMP? O 1.78 O 1.7 O 1.75 O 0.20 O 1.07Question 4 1 pts River 2: S2D Question 14 1 pts Although the degrees of freedom are different, does JMP yield the same conclusion as our methods (compare with your work by hand)? 0 Yes O No Question 5 1 pts Which of the following is the correct null and alternative hypotheses? Note: M1 signifies the population mean mercury concentration in River 1, and M2 signifies the population mean mercury concentration in River 2. O HO: M1 = 12 H1: M1 = 12 O HO: M1 = 12 H1: M1 M2x Md Sd W Note: Here, the subscript d indicates a statistic or parameter for a sample of paired differences. 0 Test stat B and Sampling Distribution: t- distribution with 59 degrees of freedom 0 Test stat C and Sampling Distribution: t- distribution with 72 degrees of freedom 0 Test stat C and Sampling Distribution: t- distribution with 59 degrees of freedom 0 Test stat A and Sampling Distribution: t- distribution with 56 degrees of freedom 0 Test stat A and Sampling Distribution: t- distribution with 128 degrees of freedom 0 Test stat A and Sampling Distribution: t- distribution with 72 degrees of freedom 0 Test stat B and Sampling Distribution: t- distribution with 72 degrees of freedom \fD Question 15 1 pts Interpret the meaning of this pvalue in the context of this problem. 0 The pvalue is the probability of observing another such random sample with test statistic having absolute value greater than the currently observed test statisb'c under the null hypothesis. 0 The p-value is the probability of observing another such random sample with test statistic less than the currently observed test statistic under the null hypothesis. 0 The p-value is the probability of observing another such random sample with test statistic greater than the currently observed test statistic. O The pvalue is the probability of observing another such random sample with test statistic greater than the currently observed test statistic under the null hypothesis. D Question 1 1 pts What are the sample mean, sample standard deviation, and sample size for mercury concentration for each river (round to TWO decimal places)? River 1: x-bar1 = \fD Question 8 1 pts Compute the test statistic by hand (provide the absolute value and round to TWO decimal places). |Test stat |=| t I: \fD Question 13 1 pts We assumed the standard deviations of the two populations were NOT the same which told us what degrees of freedom to use. Noh'ce that JIVIP does something different. The degrees of freedom JIVIP thinks we should be using is pretty far from the degrees of freedom you should have selected in question 7. The closer JMP's df is to n1+n22, the more it would be reasonable to treat the population standard deviations as equal. The closer this number is to min(n1 1, n2 1), the more necessary it is to treat the population standard deviations as different. How similar or different does JMP find the estimated standard deviations? 0 Very different 0 Fairly similar D Question 10 1 pts Do you reject or fail to reject the null hypothesis? 0 Reject O Fail to reject \fD Now we'll get JMP to do the test for us. (If you made a new data table to get the t value, close that window first and go back to your original data table.) Return to the JMP Starter window, and go to Basic and "Two- Sample t-Test". Put Mercury in "Y, Response" and put River in "X, Grouping", and hit OK. ... JMP S . . . Oneway - Distribution by Group Click Category: Basic Analysis The distribution of the response across groups defined by the categories Select Columns Cast Selected Columns into Roles Action File Distribution Basic E 6 Columns Y, Response Mercury OK Fit Model River optional numeric contin 9 8232 Predictive Modeling Station Cancel 40 Two-Sample t-Test Length Specialized Modeling Weight Screening Mercury X, Grouping River Multivariate i. Short Fish optional Remove Clustering Bivariate Analysis Recall Reliability Graph Fit Y by X Examine rela Oneway, Biv Block optional Help Surface the context Measure Oneway Weight optional numeric Control Freq optional numeric Consumer Research DOE By Tables Bivariate optional SAS JMP gives you the summary statistics, and below that the test information.Question 11 1 pts State your conclusions in the context of the problem. O There is sufficient evidence to warrant rejection of the claim that the population mean mercury concentrations of the two rivers are different. O There is not sufficient evidence to warrant rejection of the claim that the population mean mercury concentrations of the two rivers are different. O There is not sufficient sample evidence to support the claim that the population mean mercury concentrations of the two rivers are different. O The sample data support the claim that the population mean mercury concentrations of the two rivers are different