1 For each of the following situations, give the degrees of freedom for the group (DFG), for error (DFE), and for the total (DFT). State the null and alternative hypotheses, H0 and Ha, and give the numerator and denominator degrees of freedom for the F statistic. (a) A poultry farmer is interested in reducing the cholesterol level in his marketable eggs. He wants to compare two different cholesterol-lowering drugs added to the hen's standard diet as well as an allvegetarian diet. He assigns 25 of his hens to each of the three treatments. RN_3006685_0_ DFG = {"js_version":0} RN_3006685_0_ DFE = {"js_version":0} RN_3006685_0_ DFT = {"js_version":0} H0: mc All groups have different mean cholesterol levels. mean cholesterol level. All groups have the same mean cholesterol level. has a different mean cholesterol level. level. The all-vegetarian diet group has a higher At least one group The all-vegetarian diet group has a lower mean cholesterol RC_3006685_0_3 {} Ha: mc All groups have different mean cholesterol levels. cholesterol level. At least one group has a different mean The all-vegetarian diet group has a lower mean cholesterol level. have the same mean cholesterol level. All groups The all-vegetarian diet group has a higher mean cholesterol level. RC_3006685_0_4 {} RN_3006685_0_ numerator df {"js_version":0} RN_3006685_0_ denominator df {"js_version":0} (b) A researcher is interested in students' opinions regarding an additional annual fee to support nonincome-producing varsity sports. Students were asked to rate their acceptance of this fee on a sevenpoint scale. She received 95 responses, of which 31 were from students who attend varsity football or basketball games only, 15 were from students who also attend other varsity competitions, and 49 who did not attend any varsity games. RN_3006685_0_ DFG = {"js_version":0} DFE = RN_3006685_0_ {"js_version":0} RN_3006685_0_ DFT = {"js_version":0} H0: mc All groups have different mean ratings. higher mean rating. The group of students who do not attend games has a All groups have the same mean rating. attend games has a lower mean rating. The group of students who do not At least one group has a different mean rating. RC_3006685_0_1 {} Ha: mc The group of students who do not attend games has a higher mean rating. different mean ratings. All groups have the same mean rating. not attend games has a lower mean rating. RC_3006685_0_1 {} numerator df RN_3006685_0_ All groups have The group of students who do At least one group has a different mean rating. {"js_version":0} RN_3006685_0_ denominator df {"js_version":0} (c) A professor wants to evaluate the effectiveness of his teaching assistants. In one class period, the 42 students were randomly divided into three equal-sized groups, and each group was taught power calculations from one of the assistants. At the beginning of the next class, each student took a quiz on power calculations, and these scores were compared. RN_3006685_0_ DFG = {"js_version":0} RN_3006685_0_ DFE = {"js_version":0} RN_3006685_0_ DFT = {"js_version":0} H0: mc The group taught by the oldest TA has a lower mean quiz score. TA has a higher mean quiz score. The group taught by the oldest All groups have the same mean quiz score. group has a different mean quiz score. At least one All groups have different mean quiz scores. RC_3006685_0_1 {} Ha: mc The group taught by the oldest TA has a lower mean quiz score. different mean quiz score. same mean quiz score. At least one group has a All groups have different mean quiz scores. All groups have the The group taught by the oldest TA has a higher mean quiz score. RC_3006685_0_1 {} RN_3006685_0_ numerator df {"js_version":0} RN_3006685_0_ denominator df {"js_version":0} Submit Answer Save Progress Your work in question(s) will also be submitted or saved. Submit Assignment Save Assignment Progress Question 2 Many studies have suggested that there is a link between exercise and healthy bones. Exercise stresses the bones and this causes them to get stronger. One study examined the effect of jumping on the bone density of growing rats. There were three treatments: a control with no jumping, a low-jump condition (the jump height was 30 centimeters), and a high-jump condition (60 centimeters). After 8 weeks of 10 jumps per day, 5 days per week, the bone density of the rats (expressed in mg/cm 3 ) was measured. Here are the data. data474.dat (a) Make a table giving the sample size, mean, and standard deviation for each group of rats. Consider whether or not it is reasonable to pool the variances. (Round your answers for x, s, and /cgi-perl/ symimag to one decimal place.) / cgi-perl/symimag Group n / cgi-perl/ symimag s RN_2970418_1_ RN_2970418_1_ RN_2970418_1_ RN_2970418_1_ Control {"js_version":0}{"js_version":0}{"js_version":0}{"js_version":0} RN_2970418_1_ RN_2970418_1_ RN_2970418_1_ RN_2970418_1_ Low jump {"js_version":0}{"js_version":0}{"js_version":0}{"js_version":0} RN_2970418_1_ RN_2970418_1_ RN_2970418_1_ RN_2970418_1_ High jump {"js_version":0}{"js_version":0}{"js_version":0}{"js_version":0} (b) Run the analysis of variance. Report the F statistic with its degrees of freedom and P-value. What do you conclude? (Round your test statistic to two decimal places and your P-value to three decimal places.) F= RN_2970418_1_ {"js_version":0} = RN_2970418_1_ P {"js_version":0} Conclusion: There is ---Select--- RC_2970418_1_1 {"pulldown":1} statistically significant difference between the three treatment means at the = .05 level. Submit Answer Save Progress Question 3 A survey looked at the value of recreational sports on college campuses. One of the questions asked each student to rate the importance of recreational sports to college satisfaction and success. Responses were on a 10-point scale with 1 indicating total lack of importance and 10 indicating very high importance. The following table summarizes these results: n Class Freshman Sophomore Junior Senior 721 536 594 439 Mean score 7.6 7.6 7.5 7.3 (a) To compare the mean scores across classes, what are the degrees of freedom for the ANOVA F statistic? RN_2970409_2_ numerator df {"js_version":0} denominator df RN_2970409_2_ {"js_version":0} (b) The MSG = 11.106. If sp = 2.14, what is the F statistic? (Round your answer to two decimal places.) F= RN_2970409_2_ {"js_version":0} (c) Give an approximate (from Table E) or exact (from software) P-value. (Enter your answer to four decimal places.) RN_2970409_2_ Submit Answer {"js_version":0} Save Progress Question 4 Different varieties of the tropical flower Heliconia are fertilized by different species of hummingbirds. Over time, the lengths of the flowers and the form of the hummingbirds' beaks have evolved to match each other. Here are data on the lengths in millimeters of three varieties of these flowers on the island of Dominica. data491.dat Do a complete analysis that includes description of the data and a significance test to compare the mean lengths of the flowers for the three species. (Round your answers for x to four decimal places, s to three decimal places, and to three decimal places. Round your test statistic to two decimal / cgi-perl/ symimag places. Round your P-value to three decimal places.) /cgi-perl/ symimag flower type n /cgi-perl/ symimag s H. bihai RN_2970410_3_ RN_2970410_3_ RN_2970410_3_ RN_2970410_3_ {"js_version":0}{"js_version":0}{"js_version":0}{"js_version":0} RN_2970410_3_ RN_2970410_3_ RN_2970410_3_ RN_2970410_3_ H. caribaea red {"js_version":0}{"js_version":0}{"js_version":0}{"js_version":0} RN_2970410_3_ RN_2970410_3_ RN_2970410_3_ RN_2970410_3_ H. caribaea yellow {"js_version":0}{"js_version":0}{"js_version":0}{"js_version":0} F= P= RN_2970410_3_ {"js_version":0} RN_2970410_3_ {"js_version":0} Submit Answer Save Progress Question 5 Iron-deficiency anemia is the most common form of malnutrition in developing countries, affecting about 50% of children and women and 25% of men. Iron pots for cooking foods had traditionally been used in many of these countries, but they have been largely replaced by aluminum pots, which are cheaper and lighter. Some research has suggested that food cooked in iron pots will contain more iron than food cooked in other types of pots. One study designed to investigate this issue compared the iron content of some Ethiopian foods cooked in aluminum, clay, and iron pots. One of the foods was yesiga wet, beef cut into small pieces and prepared with several Ethiopian spices. The iron content of four samples of yesiga wet cooked in each of the three types of pots is given below. The units are milligrams of iron per 100 grams of cooked food. data402.dat (a) Make a table giving the sample size, mean, and standard deviation for each type of pot. Is it reasonable to pool the variances? Note that with the small sample sizes in this experiment, we expect a large amount of variability in the sample standard deviations. Type of pot n / cgi-perl/symsimag / cgi-perl/symimag RN_3563665_4_ RN_3563665_4_ RN_3563665_4_ RN_3563665_4_ Aluminum {"js_version":0}{"js_version":0}{"js_version":0}{"js_version":0} RN_3563665_4_ RN_3563665_4_ RN_3563665_4_ RN_3563665_4_ Clay {"js_version":0}{"js_version":0}{"js_version":0}{"js_version":0} RN_3563665_4_ RN_3563665_4_ RN_3563665_4_ RN_3563665_4_ Iron {"js_version":0}{"js_version":0}{"js_version":0}{"js_version":0} (b) Run the analysis of variance. Report the F statistic with its degrees of freedom and P-value. What do you conclude? (Round your test statistic to two decimal places. Round your P-value to three decimal places.) F= RN_3563665_4_ {"js_version":0} RN_3563665_4_ {"js_version":0} P= Conclusion: There is ---Select--- RC_3563665_4_1 {"pulldown":1} statistically significant difference between the three treatment means at the = .05 level. Question 6 The National Crime Victimization Survey estimates that there were over 400,000 violent crimes committed against women by their intimate partner that resulted in physical injury. An intervention study designed to increase safety behaviors of abused women compared the effectiveness of six telephone intervention sessions with a control group of abused women who received standard care. Fifteen different safety behaviors were examined. One of the variables analyzed was the total number of behaviors (out of 15) that each woman performed. Here is a summary of the means of this variable at baseline (just before the first telephone call) and at follow-up 3 and 6 months later. Time Group Baseline 3 months 6 months Intervention 10.4 12.5 11.9 Control 9.9 10.4 9.6 (a) Find the marginal means. (Round your answers to three decimal places.) Time Group Baseline 3 months 6 months Mean RN_3449975_5_ Intervention 10.4 12.5 11.9 {"js_version":0} RN_3449975_5_ Control 9.6 9.9 10.4 {"js_version":0} RN_3449975_5_ RN_3449975_5_ RN_3449975_5_ RN_3449975_5_ Mean {"js_version":0}{"js_version":0}{"js_version":0}{"js_version":0} Are they useful for understanding the results of this study? mc The row means suggest that the intervention group showed more improvement than the control group. The row means suggest that the control group showed more improvement than the 3 months group. The row means suggest that the intervention group showed more improvement than the 6 months group. The row means suggest that the control group showed more improvement than the baseline group. The row means suggest that the intervention group showed less improvement than the control group. RC_3449975_5_6 {} (b) Plot the means. Do you think there is an interaction? Describe the meaning of an interaction for this study. mc Yes there is an interaction, it means that the mean number of actions does not change over time for the two groups. Yes there is an interaction, it means that the mean number of actions changes consistently over time for the two groups. Yes there is an interaction, it means that the mean number of actions changes differently over time for the two groups. No there is not an interaction, meaning that the mean number of actions does not change over time for the two groups. RC_3449975_5_7 {} (Note: This exercise is from a repeated-measures design, and the data are not particularly normal because they are counts with values from 1 to 10. Although we cannot use the methods in this chapter for statistical inference in this setting, the example does illustrate ideas about interactions.) Submit Answer Save Progress Question 7 Do left-handed people live shorter lives than right-handed people? A study of this question examined a sample of 949 death records and contacted next of kin to determine handedness. Note that there are many possible definitions of "left-handed." The researchers examined the effects of different definitions on the results of their analysis and found that their conclusions were not sensitive to the exact definition used. For the results presented here, people were defined to be right-handed if they wrote, drew, and threw a ball with the right hand. All others were defined to be left-handed. People were classified by gender (female or male) and handedness (left or right), and a 2 2 ANOVA was run with the age at death as the response variable. The F statistics were 22.36 (handedness), 37.44 (gender), and 2.10 (interaction). The following marginal mean ages at death (in years) were reported: 77.39 (females), 71.32 (males), 75.00 (right-handed), and 66.03 (left-handed). (a) For each of the F statistics given, find the degrees of freedom and an approximate P-value. Summarize the results of these tests. (b) Using the information given, write a short summary of the results of the study. Submit Answer Save Progress Question #8 A study of undergraduate computer science students examined changes in major after the first year. The study examined the fates of 256 students who enrolled as first-year students in the same fall semester. The students were classified according to gender and their declared major at the beginning of the second year. For convenience we use the labels CS for computer science majors, EO for engineering and other science majors, and O for other majors. The explanatory variables included several high school grade summaries coded as 10 = A, 9 = A-, etc. Here are the mean high school mathematics grades for these students. Major Gender CS Males EO O 8.68 8.35 7.65 Females 9.11 9.36 8.04 Describe the main effects and interaction using appropriate graphs and calculations