(a)
Section 1:
To find: The error degrees of freedom for Model 1.
(a)
Section 1:
Answer to Problem 19E
Solution: There are 200 error degrees of freedom in Model 1.
Explanation of Solution
Calculation: The two models have been provided in the problem. Model 1 discusses the effect of Gene expression
Here, the variable
The degrees of freedom for the model are calculated as
The total degrees of freedom are calculated as:
The error degrees of freedom are calculated as
Section 2:
To find: The error degrees of freedom for Model 2.
Section 2:
Answer to Problem 19E
Solution: There are 199 error degrees of freedom in Model 2.
Explanation of Solution
Calculation: The two models have been provided in the problem. Model 2 discusses the effect of Gene expression
Here, the variable
The degrees of freedom for the model are calculated as
The total degrees of freedom are calculated as
The error degrees of freedom are calculated as
(b)
To test: The null hypothesis that “the serotonin gene regression coefficient is equal to zero” against “it is not equal to zero,” and the corresponding test statistic and its P-value in Model 1.
(b)
Answer to Problem 19E
Solution: The result is significant, that is, the regression coefficient for gene expression
Explanation of Solution
Calculation: The null hypothesis to test whether the variable gene expression
The alternative hypothesis that the variable for gene expression
The level of significance is 0.05. It is provided that
The test statistic
The critical value of test statistic
The P-value for the test is calculated as
Conclusion: The P-value is less than the level of significance. Also, the test statistic results are
Hence, the null hypothesis gets rejected, that is, the result is significant.
(c)
Section 1:
To test: The null hypothesis that “the serotonin gene regression coefficient is equal to zero” against “it is not equal to zero,” and the corresponding test statistic and its P-value for Model 2.
(c)
Section 1:
Answer to Problem 19E
Solution: The result is significant, that is, the regression coefficient for gene expression
Explanation of Solution
Calculation: The null hypothesis to test whether the regression coefficient for gene expression
The alternative hypothesis that the regression coefficient for gene expression
The level of significance is 0.05. It is provided that
The test statistic
The critical value of test statistic
The P-value for the test is calculated as
Conclusion: The P-value is less than the level of significance. Also, the test statistic results are
Hence, the null hypothesis gets rejected, that is, the result is significant.
Section 2:
To test: The null hypothesis that “the rule-breaking composite coefficient is equal to zero” against “it is not equal to zero,” and the corresponding test statistic and its P-value for Model 2.
Section 2:
Answer to Problem 19E
Solution: The result is significant, that is, the coefficient for rule-breaking composite
Explanation of Solution
Calculation: The null hypothesis to test whether the coefficient of rule-breaking composite
The alternative hypothesis that the explanatory variable rule-breaking composite
The level of significance is 0.05. It is provided that
The test statistic
The critical value of test statistic
The P-value for the test is calculated as
Conclusion: The P-value is less than the level of significance. Also, the test statistic results are
Hence, the null hypothesis gets rejected, that is, the result is significant.
(d)
Section 1
Whether there lies a positive relationship between “the serotonin gene receptor expression level” and “popularity” after adjusting for rule-breaking.
(d)
Section 1
Answer to Problem 19E
Solution: The coefficients of the variables “gene expression” and “rule breaking” are positive. It highlights that there lies a positive relationship between the coefficients of the two variables in both the models.
Explanation of Solution
It is observed from the calculations in part (c) that there lies a relationship between the serotonin gene receptor expression and the popularity after adjusting for rule-breaking. Also, it is seen that the coefficients of gene expression and rule breaking for both the models are positive.
Section 2
To find: The comparison of upsurge in popularity when the gene expression increases by one unit and the rule breaking composite remains fixed.
Section 2
Answer to Problem 19E
Solution: When the variable gene expression is increased by one unit, the popularity increases by 0.204 units in Model 1, and there is an increase in popularity by 0.161 units in Model 2.
Explanation of Solution
Calculation: The regression model for Model 1 can be written as
When the gene expression is increased by 1 unit, the increase in the popularity is calculated as follows:
Also, the regression model for Model 2 can be written as
When the gene expression is increased by 1 unit, keeping all other variables constant, the increase in popularity is calculated as follows:
Want to see more full solutions like this?
Chapter 11 Solutions
LaunchPad for Moore's Introduction to the Practice of Statistics (12 month access)
- introduces a study investigating whether a brief diet intervention might improve depression symptoms. In the study, 75 college-age students with elevated depression symptoms and relatively poor diet habits were randomly assigned to either a healthy diet group or a control group. Depression levels were measured at the beginning of the experiment and then again three weeks later. The response variable is the reduction in depression level (as measured by the DASS survey) at the end of the three weeks. Larger numbers mean more improvement in depression symptoms. Test whether these experimental results allow us to conclude that, on average, improvement of depression symptoms is higher for those who eat a healthy diet for three weeks than for those who don't. The data is available on StatKey and in DietDepression. Let Group 1 represent those with a healthy diet and Group 2 represent those with no diet change. State the null and alternative hypotheses.arrow_forwardDowns and Abwender (2002) evaluated soccer players and swimmers to determine whether the routine blows to the head experienced by soccer players produced long term neurological deficits. In the study, neurological tests were administered to mature soccer players and swimmers and the results indicated significant differences. In a similar study, a researcher obtained the following data. Swimmers Soccer Players 10 7 8 4 7 9 9 3 13 7 7 6 12 a)Are the neurological test scores significantly lower for the soccer player than for the swimmers in the control groups? Use a one-tailed test with = .05. b)Compute the value of r² (percentage of variance accounted for) these data.arrow_forwardMcAllister et al. (2012) compared varsity football and hockey players with varsity athletes from non-contact sports to determine whether exposure to head impacts during one season have an effect on cognitive performance. In the study, tests of new learning performance were significantly poorer for the contact sport athletes compared to the non-contact sport athletes. Cognitive Performance Contact Athletes Non-Contact Athletes n1 = 8 n2 = 8 M1 = 6 M2 = 9 s2 = 8 s2 = 6.23 Are the test scores significantly lower for the contact sport athletes than for the non-contact athletes? Conduct the appropriate hypothesis test using α = .05 and state your conclusion in terms of this problem. Make sure to use APA style conclusions (as shown in lecture videos).arrow_forward
- a study of the effects of color on easing anxiety cpmpared anxiety test scores of prticipants who completed the test printed on either soft yellow paper or on harsh green paper.the scores for the five participants who cpmpleted the test on the green paper were 20, 26, 28, 21, and 18. the scores for four particiopants who completed the test on green paper were 20, 26, 17, and 24. using the .05 level, one-tailed (predicting lower anxiety scores for the yellow paper), what should the researcher colclude? a. use the steps of hypothesis testingarrow_forwardIn a study conducted in the Science Department of Faculty of Science, Technology and Human Development in a University; the researcher examined the influence of the drug succinylcholine on the circulation levels of androgens in the blood. Blood samples from wild, free-ranging deer were obtained via the jugular vein immediately after an intramuscular injection of succinylcholine using darts and a capture gun. Deer were bled again approximately 30 minutes after the injection and then released. The level of androgens at time of capture and 30 minutes later, measured in nanograms per milliliter (ng/ml), for 15 deers as in Table Q1. Assuming that the populations of androgen at time of injection and 30 minutes later are normally distributed:i) Find the average and standard deviation of this studyii)Determine the critical region of this problem.iii) Test at the 0.05 level of significance whether the androgen concentrations are altered after 30 minutes of restraint.arrow_forwardAn amusement park studied methods for decreasing the waiting time (minutes) for rides by loading and unloading riders more efficiently. Two alternative loading/unloading methods have been proposed. To account for potential differences due to the type of ride and the possible interaction between the method of loading and unloading and the type of ride, a factorial experiment was designed. Use the following data to test for any significant effect due to the loading and unloading method, the type of ride, and interaction. Use ? = 0.05. Type of Ride Roller Coaster Screaming Demaon Log Flume Method 1 41 52 50 43 44 46 Method 2 49 50 48 51 46 44 Find the value of the test statistic for method of loading and unloading. Test statistic=?? Find the p-value for method of loading and unloading. (Round your answer to three decimal places.) p-value = ?? State your conclusion about method of loading and unloading. -Because the p-value ≤ ? = 0.05, method…arrow_forward
- Which of the independent variables retains the strongest association with the number of children a respondent has when all other variables in the model are controlled? What is that association? Which has the weakest when other variables are controlled?arrow_forwardIn studies examining the effect of humor on interpersonal attractions, McGee and Shevlin (2009) found that an individual’s sense of humor had a significant effect on how the individual was perceived by others. In one part of the study, female college students were given brief descriptions of a potential romantic partner. The fictitious male was described positively as being single and ambitious and having good job prospects. For one group of participants, the description also said that he had a great sense of humor. For another group, it said that he has no sense of humor. After reading the description, each participant was asked to rate the attractiveness of the man on a seven-point scale from 1 (very unattractive) to 7 (very attractive). A score of 4 indicates a neutral rating. The females who read the “great sense of humor” description gave the potential partner an average attractiveness score of M = 4.53 with a standard deviation of s = 1.04. If the sample consisted of n = 16…arrow_forwardWhat can conclude about the null hypothesis from this dataset of weight gain in mice grouped by treatments of diet type and stress level? Weight Diet Stress 10.8 C H 11 C H 9.7 C H 10.1 C H 11.2 C H 9.8 C L 10.7 C L 9.4 C L 9.9 C L 10 C L 12.8 A H 13.9 A H 11.8 A H 13 A H 12 A H 10.9 A L 13.6 A L 10.9 A L 11.5 A L 12.8 A L 9.8 B H 8.8 B H 8 B H 7.6 B H 9 B H 10 B L 8 B L 7.8 B L 7.9 B L 9.2 B Larrow_forward
- A cross-sectional study is conducted to investigate cardiovascular disease (CVD) risk factors among a sample of patients seeking medical care at one of three local hospitals. A total of 500500 patients are enrolled. Based on the following data, we would like to determine if there is a significant association between the family history of CVD and the enrollment site. Enrollment Site Family History of CVD Hospital 1 Hospital 2 Hospital 3 Total Yes 34 8 58 100 No 104 72 224 400 Total 138 80 282 500 Given: The value of the test statistic is χ2= 6.912 Use α=0.1 as the level of significance. The superintendent of Hospital 2 performed the Goodness of Fit Test to test whether 25% of the patients go to Hospital 1, 15% of the patients go to Hospital 2 and 60% of the patients go to Hospital 3. Given: The superintendent found that the pp-value for the test is 0.25091 Let: p1=p1= be the proportion of patients at Hospital 1 p2=p2= be the proportion of patients at…arrow_forwardA Canadian study measuring depression level in teens (as reported in the Journal of Adolescence, vol. 25, 2002) randomly sampled 112 male teens and 101 female teens, and scored them on a common depression scale (higher score representing more depression). The researchers suspected that the mean depression score for male teens is higher than for female teens, and wanted to check whether data would support this hypothesis. If μ1 and μ2 represent the mean depression score for male teens and female teens respectively, which of the following is an appropriate pair of hypotheses in this case? Check all that apply.arrow_forwardDo cell phones increase drivers' reaction times while driving? A 2003 American Journal of Health Education study investigated the effects of cell phone use on reaction time. In the study, 60 participants were randomly selected and placed into one of two groups: the cell phone group or the control group. Those in the control group participated in the experiment with no distractions, whereas those in the cell phone group had access to text documents on a cell phone. Participants in each group were then asked to take a computerized reaction time test. Researchers then recorded each subject's reaction time in seconds. The table shows the results of the experiment. Group Populationmean Samplesize Samplemean Sample standarddeviation Phone up n=30 x¯P=0.546 sx=0.213 Control uc n=30 x¯C=0.356 sx=0.245 df=56.900 Suppose the researchers wish to examine at a significance level of alpha=0.05 if the mean reaction time for phone users is larger than the mean reaction time for the…arrow_forward
- Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt