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Given the population 1, 3, 4, 6 and 8. Suppose samples of size 3 are drawn from this population. What is the mean and standard deviation of the Sampling Distribution?
Getting acquainted with the essential terms and concepts on correlation, it is now time for you to explain thoroughly your answers to the following questions.
1. Discuss the different kinds of relationship that are possible between two variables.
2. A study has shown that the correlation between fatigue and irritability is 0.53. Based on this correlation, the author concludes that fatigue is an important factor in producing irritability. Is this conclusion justified? Explain.
CORRELATION.
1. A graduate student in developmental psychology believes there may be a relationship between birth weight and subsequent IQ. She randomly samples seven psychology majors at her university and gives them an IQ test. Next, she obtains the weight at birth of the seven majors from the appropriate hospitals (after obtaining permission from the students, of course). The data are shown in the following table.
Student: 1 2 3 4 5 6 7
Birth Weight: 5.8 6.5 8.0 5.9 8.5 7.2 9.0
IQ: 122 120 129 112 127 116 130
a. Construct a scatter plot of the data, plotting birth weight on the X axis and IQ on the Y axis. Does the relationship appear to be linear?
b. Assume the relationship is linear and compute the value of Pearson r.
TWO DEPENDENT SAMPLE MEANS.
Use the traditional method in testing hypothesis.
Developmental psychologists at a prominent California university conducted a longitudinal study investigating the effect of high levels of curiosity in early childhood on intelligence. The local population of 3-year-olds was screened via a test battery assessing curiosity. Twelve of the 3-year-olds scoring in the upper 90% of this variable were given an IQ test at age 3 and again at age 11. The following IQ scores were obtained.
Student Number: 1 2 3 4 5 6 7 8 9 10 11 12
IQ (Age of 3) : 100 105 125 140 108 122 117 112 135 128 104 98
IQ (Age of 11) : 114 116 139 151 106 119 131 136 148 139 122 113
Using ∝= 0.01, two-tailed test, analyse the data and then interpret the result.
Based on the concept on Analysis of Variance (ANOVA) and the learning exercises that you have done, write your arguments or lessons learned below.
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Getting acquainted with the essential terms and concepts on Analysis of Variance (ANOVA), it is now time for you to explain thoroughly your answers to the questions found below.
1. Explain the usage of the following statistical tools in testing the hypotheses.
a. Testing One Sample Mean using t-test and z-test.
b. Testing Two Independent Sample Mean.
c. Testing Dependent Sample Mean.
d. Analysis of Variance
A sleep researcher conducts an experiment to determine whether sleep loss affects the ability to maintain sustained attention. Fifteen individuals are randomly divided into the following three groups of five subjects each: group 1, which gets the normal amount of sleep (7–8 hours); group 2, which is sleep-deprived for 24 hours; and group 3, which is sleep-deprived for 48 hours. All three groups are tested on the same auditory vigilance task. Subjects are presented with half-second tones spaced at irregular intervals over 1-hour duration. Occasionally, one of the tones is slightly shorter than the rest. The subject’s task is to detect the shorter tones. The following percentages of correct detection were observed:
Normal Sleep: 85 83 76 64 75
Sleep-Deprived for 24-hours: 60 58 76 52 63
Sleep-Deprived for 48-hours: 60 48 38 47 50
Determine whether there is an overall effect for sleep deprivation, using the conceptual equations of the one-way ANOVA. Use ∝= 0.05.
The management of Resale Furniture, a change of second hand furniture stores in Metro Manila, designed an incentive plan for salespeople. To evaluate this innovative incentive plan, 10 salespeople were selected at random, and their weekly incomes before and after the incentive plan were recorded.
SALE PERSON 1
Before: 2000
After: 3500
SALE PERSON 2
Before: 3000
After:4120
SALE PERSON 3
Before: 2500
After: 3800
SALE PERSON 4
Before: 3100
After: 4200
SALE PERSON 5
Before: 1900
After: 1820
SALE PERSON 6
Before: 1750
After: 1600
SALE PERSON 7
Before: 2300
After: 3400
SALE PERSON 8
Before: 3210
After: 1900
SALE PERSON 9
Before: 2340
After: 2340
SALE PERSON 10
Before: 1870
After: 3290
Was there a significant increase in the typical salesperson's weekly income due to the innovative incentive plan? Use the 0.05 level of significance.
