Statistics 2480 HOMEWORK ASSIGNMENT #10 1. The types of browse favored by deet a
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Statistics 2480 HOMEWORK ASSIGNMENT #10 1. The types of browse favored by deet are shown in the folle 1. The types of browse favored by deer ate shown in the following table (The Mule Deer of Mesa L erde observed inoculars oh National paredited by Mior au and Schmidt). Moro recently, volunteers using b the feeding habits of a random sample of 320 deer Do these data suggest that the published deer feeding pattern follows the natural distribution of browse (plants), or is there evidence to suggest that the deer favor a particular browse (plant) Plant Composition Observed Number of Deer in Study Area Type of Brow Sage Rabbit brush Salt brush Service berry Other Feeding on This Plant 102 125 43 27 23 se 40% 10% 10% 10% 2. Chronic lung discase is one of the primary long-term complications among premature infants. A research hypothesis suggested that the use of inhaled nitric oxide would decrease the ineidence of chronic lung disease and death in premature infants. To test this hypothesis, a randomized, double- blind, placebo-controlled study of inhaled nitric oxide versus placebo in premature infants undergoing mechanical ventilation was designed and conducted. A total of 105 infants were assigned to the treatment group, and 102 infants were assigned to the control group. Results for the primary endpoint death and chronic lung disease- are shown in the talbe below Is there statistically significant evidence that nitric oxide is reducing the incidence of death or chronic lung disease among premature infants undergoing mechanical ventilation? Nitric Oxide Placebo Survival without chronic lung disease Death or chronic lung disease Total 54 51 105 37 65 102 3. Many studies have found a relationship between eating breakfast and academic performance in chil- dren. You want to test this using a randon sample of students at a nearby middle school. You asked each student in your sample, "Did you eath breakfast this morning" and you observed whether the child was (mostly) paying attention during the math lesson that day. The data are provided below a. Conduct the appropriate chi-square test to address the question posed above. b. Can we use this data to determine whether eating or not cating breakfast affects a child's ability to concentrate on a math lesson? Yes - Pay Attention No- Do Not Pay Attention Breakfast this morning? Yes Breakfast this morning? No 19 15Explanation / Answer
As the significance level is not given, we assume it is 0.05.
As there are 320 deer, then we multiply each percentage by 320 to get the expected values,
Doing an observed/expected value table,
Using chi^2 = Sum[(O - E)^2/E],
chi^2 = 7.5390625
As df = a - 1,
a = 5
df = a - 1 = 4
Then, the critical chi^2 value is
significance level = 0.05
chi^2(crit) = 9.487729037
Also, the p value is
p = 0.109999086
As chi^2 < 9.488, and P > 0.05, we FAIL TO REJECT THE NULL HYPOTHESIS.
Thus, there is no significant evidence that the deer favor a particular browse at 0.05 level. [CONCLUSION]
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O E (O - E)^2/E 102 96 0.375 125 128 0.070313 43 32 3.78125 27 32 0.78125 23 32 2.53125