Question

The following data represent the level of health and the level of education for a random sample of 1504 residents. Complete parts​ (a) and​ (b) below. Education Excellent Good Fair Poor Not a H.S. graduate 89 151 52 112 H.S. graduate 86 101 53 100 Some college 81 132 66 108 Bachelor Degree or higher 58 147 60 108 ​(a) Does the sample evidence suggest that level of education and health are independent at the alphaequals0.05 level of​ significance? Conduct a​ P-value hypothesis test. State the hypotheses. Choose the correct answer below. A. Upper H 0​: Level of education and health are independent. Upper H 1​: Level of education and health are dependent. B. Upper H 0​: p1equalsp2equalsp3 Upper H 1​: At least one of the proportions are not equal. C. Upper H 0​: mu1equalsE1 and mu2equalsE2 and mu3equalsE3 and mu4equalsE4 Upper H 1​: At least one mean is different from what is expected. Calculate the test statistic. chi Subscript 0 Superscript 2equals nothing ​(Round to three decimal places as​ needed.) The​ P-value is nothing. ​(Round to three decimal places as​ needed.) Make the proper conclusion. Choose the correct answer below. A. Reject Upper H 0. There is sufficient evidence that level of education and health are associated. B. Reject Upper H 0. There is not sufficient evidence that level of education and health are associated. C. Fail to reject Upper H 0. There is sufficient evidence that level of education and health are associated. D. Fail to reject Upper H 0. There is not sufficient evidence that level of education and health are associated. ​(b) Construct a conditional distribution of health by level of education and draw a bar graph. Education Excellent Good Fair Poor Not a H.S. graduate nothing nothing nothing nothing H.S. graduate nothing nothing nothing nothing Some college nothing nothing nothing nothing Bachelor Degree or higher nothing nothing nothing nothing ​(Round to three decimal places as​ needed.) Choose the correct bar graph below. A. A side-by-side bar graph has a vertical axis labeled from 0 to 0.5 in increments of 0.1 and a horizontal axis labeled with four education levels. The bar graph contains four vertical bars above each horizontal axis label; the four bars in each set are labeled as follows from left to right: E, G, F, P. From left to right, the vertical bars in each set have approximate heights as follows, where for each set of four bars the horizontal axis label is listed first and individual bar heights are listed from left to right: "Not H S Grad," 0.28, 0.13, 0.37, 0.22; "H S Grad," 0.29, 0.16, 0.25, 0.3; "Some College," 0.34, 0.17, 0.28, 0.21; "Bachelor," 0.16, 0.29, 0.16, 0.39. 0 0.5 E E E E G G G G F F F F P P P P Not HS Grad HS Grad Some College Bachelor B. A side-by-side bar graph has a vertical axis labeled from 0 to 0.5 in increments of 0.1 and a horizontal axis labeled with four education levels. The bar graph contains four vertical bars above each horizontal axis label; the four bars in each set are labeled as follows from left to right: E, G, F, P. From left to right, the vertical bars in each set have approximate heights as follows, where for each set of four bars the horizontal axis label is listed first and individual bar heights are listed from left to right: "Not H S Grad," 0.22, 0.37, 0.13, 0.28; "H S Grad," 0.25, 0.3, 0.16, 0.29; "Some College," 0.21, 0.34, 0.17, 0.28; "Bachelor," 0.16, 0.39, 0.16, 0.29. 0 0.5 E E E E G G G G F F F F P P P P Not HS Grad HS Grad Some College Bachelor Click to select your answer(s).

Education   Excellent   Good   Fair   Poor
Not a H.S. graduate   89   151   52   112
H.S. graduate   86   101   53   100
Some college   81   132   66   108
Bachelor Degree or higher   58   147   60   108

Answer 1

a)

option A) is correct
A. Upper H 0​: Level of education and health are independent. Upper H 1​: Level of education and health are dependent.

Test statistic = 16.704

df = 9

p-value = =chisq.dist.rt(16.704,9)

= 0.0536

option D) is correct

D. Fail to reject Upper H 0. There is not sufficient evidence that level of education and health are associated