In context. the negative relationship (shown in the scatterplot above) means that: Q The more southern the state. the higher the melanoma death rate. Q The more northern the state, the higher the melanoma death rate. 0 The more southern the state, the more people died of melanoma. The first three questions refer to the following information: The mortality rate from melanoma (skin cancer} during the 19505 was recorded for each of the 48 contiguous United States, plus Washington D.C. {as reported by Fisher and Van Belle (1993) and found on http:l/www.stat.psu.edul~lsimonlstat501wc/spOSIdatai ). The following is the scatterplot of the data: Scatterplot - 225 : r=-.83 O = 200 _ o o a o 0 o E . o o a 125 0 O "' o o a o \" o 0 . . ,_ 15o . 0 5 0 o o a ' . 9 . t ' 3- o o e 125 u _ E o o - o o 0 O 100 0 3o 35 4o 45 5o Latitude Based on the scatterplot and the value ofthe correlation coefcient. it would make sense to test the signicance of this observed linear relationship between latitude and melanoma mortality rate. The appropriate hypotheses are: I I Ha: melanoma mortality rate is related to latitude Ha: melanoma mortality rate is not related to latitude ._ _. Hg: melanoma mortality rate is not related to latitude Ha: melanoma mortality rate is related to latitude Ha: melanoma mortality rate is linearly related to latitude Ha: melanoma mortality rate is not linearly related to latitude I _;. Hg: melanoma mortality rate is not linearly related to latitude Ha: melanoma mortality rate is linearly related to latitude The following output is available: Regression Analysis: Mort versus Lat The regression equation is Mort = 389 5.98 Lat Predictor Coef SE Coef T P Constant 389.19 23.81 16.34 8.888 Lat -5.9??6 8.5984 -9.99 8.888 Ff. the data do not provide sufcient evidence to conclude that melanoma mortality rate is linearly related to latitude. Ff. the data provide extremely strong evidence that melanoma mortality rate is linearly related to latitude. (H) the data provide moderately strong evidence that melanoma mortality rate is linearly related to latitude. What is the expected count of students with high extra-curricular participation and good grades? r}. 3 .. 5.86 (:1. a f\". 1 1 2 r\". None of the above. The following four questions refer to the following information: To determine if there is a relationship between grade performance and extracurricular participation, North Carolina state conducted a study of 1 12 students, recording the number of students in each of three extra-curricular categories, and each of two grade categories. Here are the results: Good grades Poor grades Low extra-curricular participation 11 2 Moderate extra-curricular participation 68 23 High extra-curricular participation 3 5 The count that you found in the previous question is the number of students with high extra-curricular participation and good grades that you would expect to see assuming that: r\". the conditions that allow us to safely use the chi-squared procedure are met. 0. extracurricular participation and grade performance are related. ("in extracurricular participation and grade performance are independent. ("3 the null hypothesis ofthe chisquared test for independence in this case is true. r\". both (C) and (D) are correct. The following is the (edited) output of the chi-squared test in this case: Chi-Square Test: Good, Poor Expected counts are printed below observed counts ChiSquare contributions are printed below expected counts Good Poor Total Low 11 2 13 9. 52 3 . 48 8.231 8. 631 Moderate 68 23 91 66. 63 24. 38 8.828 8. 878 High 3 5 a 2.14 1. 394 3. 818 Total 82 so 112 ChiSq = 5.171, DF = 2, PValue = 0.045 ("1. the data provide sufcient evidence to conclude that extracurricular participation and grade performance are independent. (W, the data do not provide sufcient evidence to conclude that extracurricular participation and grade performance are independent. (:1 the data provide sufcient evidence to conclude that extracurricular participation and grade performance are related. ("3 the data do not provide sufcient evidence to conclude that extracurricular participation and grade performance are related. Which of the following facts should make you the most worried about the reliability of the results ofthe test in this case? ('7. The 112 students were all students in a chemical engineering course and not a random sample from the entire student body. ('5. Two of the six observed counts are less than 5. If\") Not all of the cells' contributions to the chi~squared statistic are greater than 1. (3 Two of the six expected counts are less than 5