PSY-380 Introduction to Probability and Statistics Project 3 Answer each question completely. Copy and Paste the SPSS output into the word document for the calculations portion of the problems,...

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PSY-380 Introduction to Probability and Statistics Project 3 Answer each question completely. Copy and Paste the SPSS output into the word document for the calculations portion of the problems, highlighting correct answers. (Please remember to answer the questions you must interpret the SPSS output). 1. A researcher is interested to learn if there is a linear relationship between the hours in a week spent exercising and a person’s life satisfaction. The researchers collected the following data from a random sample, which included the number of hours spent exercising in a week and a ranking of life satisfaction from 1 to 10 ( 1 being the lowest and 10 the highest). Participant Hours of Exercise Life Satisfaction 1 3 1 2 14 2 3 14 4 4 14 4 5 3 10 6 5 5 7 10 3 8 11 4 9 8 8 10 7 4 11 6 9 12 11 5 13 6 4 14 11 10 15 8 4 16 15 7 17 8 4 18 8 5 19 10 4 20 5 4 a. Find the mean hours of exercise per week by the participants. b. Find the variance and standard deviation of the hours of exercise per week by the participants. c. Run a bivariate correlation to determine if there is a linear relationship between the hours of exercise per week and the life satisfaction. Report the results of the test statistic using correct APA formatting. d. Run a linear regression on the data. Report the results, using correct APA formatting. Identify the amount of variation in the life satisfaction ranking that is due to the relationship between the hours of exercise per week and the life satisfaction (Hint: the R2 value) e. Report a model of the linear relationship between the two variables using the regression line formula. 2. Insomnia has become an epidemic in the United States. Much research has been done in the development of new pharmaceuticals to aide those who suffer from insomnia. Alternatives to the pharmaceuticals are being sought by sufferers. A new relaxation technique has been tested to see if it is effective in treating the disorder. Sixty insomnia sufferers between the ages of 18 to 40 with no underlying health conditions volunteered to participate in a clinical trial. They were randomly assigned to either receive the relaxation treatment or a proven pharmaceutical treatment. Thirty were assigned to each group. The amount of time it took each of them to fall asleep was measured and recorded. The data is shown below. Run an independent samples t-test to determine if the relaxation treatment is more effective than the pharmaceutical treatment at a level of significance of 0.05. Report the test statistic using correct APA formatting and interpret the results. Relaxation Pharmaceutical 98 20 117 35 51 130 28 83 65 157 107 138 88 49 90 142 105 157 73 39 44 46 53 194 20 94 50 95 92 161 112 154 71 75 96 57 86 34 92 118 75 41 41 145 102 148 24 117 96 177 108 119 102 186 35 22 46 61 74 75 3. A researcher is interested to learn if the level of interaction a women in her 20s has with her mother influences her life satisfaction ratings. Below is a list of women who fit into each of four levels of interaction. Conduct a One-way ANOVA on the data to determine if there are differences between groups; does the level of interaction influence women’s ratings of life satisfaction? Report the results of the One-way ANOVA. If significance is found, run the appropriate post-hoc test and report between what levels the significant differences were found. Report the test statistic using correct APA formatting and interpret the results. No Interaction Low Interaction Moderate Interaction High Interaction 2 3 3 9 4 3 10 10 4 5 2 8 4 1 1 5 7 2 2 8 8 2 3 4 1 7 10 9 1 8 8 4 8 6 4 1 4 5 3 8 4. Are handedness and gender related? A researcher collected the following data in hopes of discovering if handedness and gender are independent (Ambidextrous individuals were excluded from the study). Use the Chi-Square test for independence to explore this at a level of significance of 0.05. Report the test statistic using correct APA formatting and interpret the results.   Left-Handed Right-Handed Men 13 22 Women 27 18 5. A researcher is interested in studying the effect that the amount of fat in the diet and amount of exercise has on the mental acuity of middle-aged women. The researcher used three different treatment levels for the diet and two levels for the exercise. The results of the acuity test for the subjects in the different treatment levels are shown below.   Diet     Exercise<30% fat="" 30%="" -="" 60%="" fat="">60% fat<60 minutes 4 3 2   4 1 2   2 2 2   4 2 2   3 3 1 60 minutes 6 8 5 or more 5 8 7   4 7 5   4 8 5   5 6 6 a. perform a two-way analysis of variance (anova) and report the results using correct apa style; report whether significance was found for factor a, factor b, and/or an interaction between factors a and b was found. b. if the test statistic is significant, run a post hoc test to determine between what groups significance was found. c. report an effect size for all significant results. © grand canyon university 20155 minutes="" 4="" 3="" 2=""  ="" 4="" 1="" 2=""  ="" 2="" 2="" 2=""  ="" 4="" 2="" 2=""  ="" 3="" 3="" 1="" 60="" minutes="" 6="" 8="" 5="" or="" more="" 5="" 8="" 7=""  ="" 4="" 7="" 5=""  ="" 4="" 8="" 5=""  ="" 5="" 6="" 6="" a.="" perform="" a="" two-way="" analysis="" of="" variance="" (anova)="" and="" report="" the="" results="" using="" correct="" apa="" style;="" report="" whether="" significance="" was="" found="" for="" factor="" a,="" factor="" b,="" and/or="" an="" interaction="" between="" factors="" a="" and="" b="" was="" found.="" b.="" if="" the="" test="" statistic="" is="" significant,="" run="" a="" post="" hoc="" test="" to="" determine="" between="" what="" groups="" significance="" was="" found.="" c.="" report="" an="" effect="" size="" for="" all="" significant="" results.="" ©="" grand="" canyon="" university="" 2015="">
Answered 3 days AfterApr 14, 2021

Answer To: PSY-380 Introduction to Probability and Statistics Project 3 Answer each question completely. Copy...

Prajna answered on Apr 18 2021
147 Votes
PSY-380 Introduction to Probability and Statistics
Project 3
Answer each question completely. Copy and Paste the SPSS output into the word document for the calculations portion of the problems, highlighting correct answers. (Please remember to answer the questions you must interpret the SPSS output).
1. A researcher is interested to learn if there is a linear relationship
between the hours in a week spent exercising and a person’s life satisfaction. The researchers collected the following data from a random sample, which included the number of hours spent exercising in a week and a ranking of life satisfaction from 1 to 10 ( 1 being the lowest and 10 the highest).
    Participant
    Hours of Exercise
    Life Satisfaction
    1
    3
    1
    2
    14
    2
    3
    14
    4
    4
    14
    4
    5
    3
    10
    6
    5
    5
    7
    10
    3
    8
    11
    4
    9
    8
    8
    10
    7
    4
    11
    6
    9
    12
    11
    5
    13
    6
    4
    14
    11
    10
    15
    8
    4
    16
    15
    7
    17
    8
    4
    18
    8
    5
    19
    10
    4
    20
    5
    4
    Descriptive Statistics
    
    Mean
    Std. Deviation
    N
    Life_Satisfaction
    5.05
    2.481
    20
    Hours_of_Exercise
    8.85
    3.660
    20
a. Find the mean hours of exercise per week by the participants.
Ans: 8.85 hours
b. Find the variance and standard deviation of the hours of exercise per week by the participants.
Ans: variance = (3.660)2 = 13.3956 hours2 & standard deviation = 3.660 hours
c. Run a bivariate correlation to determine if there is a linear relationship between the hours of exercise per week and the life satisfaction. Report the results of the test statistic using correct APA formatting.
    Correlations
    
    
    Life_Satisfaction
    Hours_of_Exercise
    Pearson Correlation
    Life_Satisfaction
    1.000
    -.103
    
    Hours_of_Exercise
    -.103
    1.000
    Sig. (1-tailed)
    Life_Satisfaction
    .
    .332
    
    Hours_of_Exercise
    .332
    .
    N
    Life_Satisfaction
    20
    20
    
    Hours_of_Exercise
    20
    20

Hypothesis of interest: H0 : ρ = 0 vs. H1 : ρ > 0 or simply, in words, we take the null hypothesis as the correlation between hours of exercise and life satisfaction to be zero against the alternative hypothesis that there is a positive correlation between hours of exercise and life satisfaction.
Clearly, here one tailed test would be appropriate.
From the output above we see that the p-value has come out to be 0.332 which is greater than both 0.05 and 0.01. Hence we fail to reject the null hypothesis at 5% level of significance, even at 1% level of significance.
So, we may conclude that there is hardly any linear relationship between the hours of exercise per week and the life satisfaction as the correlation between them can be considered as zero.
d. Run a linear regression on the data. Report the results, using correct APA formatting. Identify the amount of variation in the life satisfaction ranking that is due to the relationship between the hours of exercise per week and the life satisfaction (Hint: the R2 value)
    Model Summary
    Model
    R
    R Square
    Adjusted R Square
    Std. Error of the Estimate
    Change Statistics
    
    
    
    
    
    R Square Change
    F Change
    df1
    df2
    Sig. F Change
    1
    .103a
    .011
    -.044
    2.535
    .011
    .195
    1
    18
    .664
    a. Predictors: (Constant), Hours_of_Excercise
    
    
    
    
    
The R2 value of 0.011 says that only 1.1% variation in the life satisfaction ranking is due to the relationship between the hours of exercise per week and the life satisfaction.
In fact, the Adjusted R Square value -0.044 implies that it does a terrible job at predicting Life Satisfaction by using the Hours of Exercise per week. Almost none of the variation in Life Satisfaction is explained by one’s Hours of Exercise per week.
e. Report a model of the linear relationship between the two variables using...
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