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Statistics is an area of Mathematics that uses large amounts of numerical data to make inferences based on probabilities.

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doreen.fonseca10 asked for the first time
in Statistics·
26 Apr 2022

Maintaining your balance may get harder as you grow older. A study was conducted to see how steady the elderly are on their feet. They had a random sample of subjects stand on a force platform and have them react to a noise. The force platform then measured how much they swayed forward and backward, and the data are in the table below. Do the data show that the mean elderly sway measurement is higher than the mean forward sway of younger people, which is 18.125 mm? Test at the 7% level.

forward sway in mm 18 31 1 12 17 10 19 29 17 16 27 25 27 33 3 17 14 30 22 29 14 33 26 19 20 31 31 17 8 23 9 27 34 11 36 31 30 10 10 33

P: Parameter

     What is the correct parameter symbol for this problem?

      ?   N   X   s   μ   p̂   n   σ   p   X̄  

     What is the wording of the parameter in the context of this problem?

      Select an answer   40 randomly selected elderly people   All elderly people   A randomly selected elderly person   The mean forward sway of all elderly people   The forward sway of a randomly selected elderly person   The mean forward sway in 40 randomly selected elderly people  

H: Hypotheses

     Fill in the correct null and alternative hypotheses:


H0:H0:  ?   X̄   n   σ   μ   p   X   p̂   N   s    ?   ≥   <   =   ≤   ≠   >   18.125 mm 

HA:HA:  ?   p   n   p̂   μ   N   X̄   X   σ   s    ?   <   >   =   ≥   ≤   ≠   18.125 mm 


A:  Assumptions

     Since  Select an answer   qualitative   quantitative   information was collected from each object, what conditions do we need to check?

     Check all that apply.

    

    1. no outliers in the data
    2. n(pˆ)≥10n(p̂)≥10



     Check those assumptions:

     1. Is the value of σσ known?  ?   yes   no  

 

 

 

 

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chrischad3 asked for the first time
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almas8 answered this question
in Statistics·
7 Apr 2022

No. STRAND MODALITY GWA ARS
1 ABM OBL 90 1
2 STEM OBL 90 2
3 STEM CBL 87 1
4 STEM OBL 90 1
5 STEM OBL 91 1
6 ABM CBL 90 1
7 STEM OBL 94 2
8 STEM OBL 93 2
9 ABM OBL 89 1
10 STEM CBL 87 2
11 ABM CBL 87 2
12 ABM OBL 89 2
13 ABM OBL 89 1
14 ABM CBL 83 3
15 STEM OBL 95 0
16 HUMSS OBL 90 1
17 HUMSS OBL 89 1
18 HUMSS OBL 89 1
19 STEM OBL 89 0
20 HUMSS CBL 90 1
21 HUMSS OBL 92 0
22 HUMSS CBL 84 3
23 HUMSS CBL 86 2
24 HUMSS OBL 90 1
25 STEM CBL 93 1
26 STEM CBL 95 1
27 STEM CBL 87 3
28 STEM OBL 94 0
29 HUMSS OBL 85 3
30 STEM OBL 88 2
31 ABM CBL 80
3
32 STEM OBL 88
3
33 13 HUMSS CBL 83
3
34 STEM OBL 88
2
35 ABM OBL 88
2
36 STEM CBL 85
3
37 STEM CBL 80
3
38 STEM CBL 82
3
39 STEM OBL 87
3
40 STEM OBL 88
2
41 STEM CBL 86
1
42 STEM OBL 92
1
43 HUMSS CBL 87
2
44 ABM OBL 90
2
45 STEM OBL 93
0
46 STEM OBL 92
1
47 STEM CBL 84
2
48 STEM CBL 84
3
49 ABM OBL 85
3
50 ABM CBL 86
2
51 STEM OBL 91
0
52 HUMSS CBL 82
3
53 HUMSS CBL 80
3
54 ABM OBL 85
3
55 STEM OBL 88
2
56 STEM OBL 87
2
57 STEM CBL 84
3
58 STEM OBL 91
1
59 25 ABM CBL 81
3
60 ABM OBL 90
1
61 ABM OBL 87
2
62 ABM OBL 87
2
63 STEM OBL 85
3
64 STEM OBL 86
2
65 ABM OBL 86
2
66 ABM OBL 93
0
67 STEM CBL 87
2
68 STEM OBL 88
1
69 ABM OBL 89
0
70 ABM OBL 89
1
71 STEM OBL 91
2
72 STEM CBL 85
1
73 HUMSS OBL 93
1
74 STEM CBL 89
1
75 STEM OBL 86
2
76 STEM OBL 85
3
77 HUMSS OBL 85
2
78 STEM OBL 91
1
79 STEM OBL 86
2
80 STEM CBL 83
2
81 STEM OBL 94
0
82 ABM CBL 82
3
83 STEM OBL 89
1
84 ABM OBL 86
2
85 STEM OBL 87
2
86 STEM CBL 83
3
87 STEM OBL 85
2
88 STEM OBL 88
2
89 STEM CBL 85
3
90 STEM OBL 88
2
91 ABM OBL 94
0
92 ABM OBL 85
3
93 ABM CBL 88
2
94 STEM CBL 86
2
95 STEM OBL 85
3
96 STEM OBL 86
2
97 STEM OBL 85
3
98 STEM OBL 92
1
99 ABM CBL 90
0
100 STEM CBL 81
3
101 HUMSS OBL 89
1
102 STEM CBL 88
3
103 HUMSS CBL 85
3
104 STEM OBL 89
0
105 STEM OBL 87
2
106 STEM OBL 89
1
107 STEM OBL 95
1
108 HUMSS CBL 84
3
109 STEM CBL 81
3
110 STEM OBL 86
2
111 STEM OBL 89
1
112 STEM OBL 91
1
113 STEM OBL 91
1
114 STEM CBL 89
1
115 STEM CBL 83
3
116 STEM OBL 91
3
117 STEM OBL 95
1
118 STEM OBL 87
1
119 STEM OBL 87
2
120 STEM OBL 89
0
121 STEM OBL 88
1
122 STEM OBL 91
1
123 STEM OBL 92
0
124 ABM CBL 84
3
125 STEM OBL 84
3
126 STEM CBL 83
3
127 STEM CBL 88
2
128 STEM OBL 92
1
129 STEM OBL 85
3
130 STEM CBL 87
2
131 STEM OBL 91
0
132 STEM OBL 88
2
133 STEM OBL 89
1
134 STEM CBL 88
2
135 STEM CBL 82
3
136 STEM OBL 88
2
137 HUMSS OBL 89
1
138 STEM OBL 92
1
139 ABM OBL 92
0
140 STEM OBL 92
0
141 ABM OBL 84
3
142 ABM OBL 88
1
143 HUMSS OBL 88
2
144 STEM OBL 90
1
145 HUMSS OBL 90
0
146 HUMSS OBL 90
1
147 STEM OBL 89
1
148 HUMSS OBL 94
0
149 STEM OBL 86
2
150 STEM OBL 90
0
151 ABM OBL 86
3
152 STEM OBL 86
3
153 STEM OBL 92
0
154 STEM OBL 90
1
155 STEM OBL 92
1
156 HUMSS OBL 86
3
157 STEM OBL 93
1
158 ABM OBL 86
2
159 ABM OBL 91
2
160 ABM OBL 93
2
161 ABM OBL 87
1
162 ABM OBL 87
2
163 ABM OBL 95
0
164 ABM OBL 86
2
165 STEM OBL 91
1
166 ABM OBL 87
2
167 ABM OBL 88
2
168 ABM OBL 93
0
169 HUMSS OBL 87
2
170 HUMSS OBL 84
3
171 HUMSS OBL 93
1
172 STEM OBL 84
3
173 STEM OBL 92
1
174 ABM OBL 83
3
175 HUMSS OBL 94
1
176 ABM OBL 91
1
177 HUMSS OBL 85
3
178 ABM OBL 86
2
179 STEM OBL 90
1
180 STEM OBL 84
3
181 STEM OBL 88
2
IRS LRS SRS DRS GARS
0 1 0 0 2
0 2 1 0 1
1 1 1 2 2
0 1 0 1 1
1 0 0 2 1
0 1 1 0 1
1 1 0 0 1
0 2 1 0 1
0 1 0 1 1
2 1 1 2 2
1 1 1 1 2
0 1 0 0 2
0 1 2 1 1
2 3 2 3 3
0 0 0 0 1
0 1 1 0 1
1 1 0 0 3
0 1 1 1 1
0 1 1 2 2
0 1 2 0 1
0 0 0 1 2
2 2 1 3 2
2 2 2 2 2
0 1 0 1 1
0 0 0 0 2
0 1 0 1 2
1 3 1 2 1
 Students experience tremendous levels of stress throughout their education. A high level of stress may have a negative effect on the cognitive functioning and 
learning of students. The school administration of CSU - Laboratory High School - Senior High (CSU-LHS-SH) sought to determine the levels and primary sources of 
stress and its possible correlation with the General Weighted Average (GWA) in its department. As a statistician, your task is to conduct hypothesis testing to analyze 
the gathered data. Data were collected from students of CSU-LHS-SH during the first semester of the academic year 2021 - 2022.. The Student Stressor 
Questionnaire (SSQ) was used to collect the data. 
 The SSQ contains 20 items that cover six subscales: (Academic-Related Stressors (ARS), Intrapersonal and Interpersonal Related Stressors (IRS), LearningRelated Stressors (LRS), Social-Related Stressors (SRS), Drive- and Desire-Related Stressors (DRS), and Group Activity-Related Stressors (GARS). Items in the 
SSQ represent 20 events that might be sources of stress (eg, “lack of time to review what has been learnt”, “heavy workload”). The responses were measured on a 
four-point Likert scale: “0=causing no stress”, “1=causing mild stress”, “2=causing high stress”, or “3=causing severe stress”.
 The findings of this study will contribute to the educational literature on the effect of stress on students’ academic performance, thus it must be accurate and timely.
What percent of the senior high school students have GWA below 90? 
A. 0.2843 B. 0.4257 C. 0.5743 D. 0.7157

12. What percent of senior high school students have a GWA above 87? 
A. 0.2944 B. 0.3859 C. 0.6141 D. 0.7056

13. What percent of senior high school students have a grade between 87 and 90? 
A. 0.3298 B. 0.3859 C. 0.6702 D. 0.7157

14. What grade divides the group such that 30% of the students have a grade above 
it? 
A. 85. 01 B. 86.21 C. 88.26 D. 89.81

15. What grade do we find the lowest 10% of the grade? 
A. 80. 26 B. 83.60 C. 90.04 D. 92.44

16. Between what grades contain the middle 50% of the data? 
A. 86-88 B. 86-90 C. 87-88 D. 88-90

17. What percent of ABM students have a grade above 85?
A. 0.1922 B. 0.2148 C. 0.7852 D. 0.8079 

18. What percent of HUMSS students have a grade below 89? 
A. 0.2849 B. 0.3517 C. 0.6103 D. 0.6406

19. What percent of STEM students have a grade between 85 and 89? 
A. 0.1712 B. 0.4160 C. 0.5840 D. 0.5871

20. How many students have a grade between 85 and 89? 
A. 34 B. 76 C. 105 D. 110

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almas8 answered this question
in Statistics·
30 Mar 2022

classify each of the variables as categorical (A) or numerical. If the variable is numerical, classify further as discrete (B) or continuous (C).
4. Strand                6. Students’ GWA
5. Modality            7. Students’ level of stress

For items 8-15, suppose four students are selected at random from the gathered date. Let C 
be the random variable representing the number of CBL students that are selected.

8. How many sample points can be generated from the experiment?
A. 2 B. 4 C. 16 D. 20

9. What are the values of the random variable C?
A. 0, 1, 2, 3, 4 C. 0.0625, 0.25, 0.375
B. 1, 1, 4, 4, 6 D. O and C

10. What is the probability that 2 CBL students are selected?
A. 3/16 B. 3/14 C. 3/12 D. 3/8

11. What is the probability that all students selected are OBL?
A. 0 B. 0.0625 C. 0.25 D. 1

12. What is the probability that 3 or more CBL students are selected? (2 points)
A. 0 B. 0.0625 C. 0.25 D. 0.3125

13. What is the average number of CBL students that have been selected? (2 points)
A. 1 B. 2 C. 3 D. 4

14. What is the standard deviation of the probability distribution of the number of CBL students that has been selected? (2 points)
A. 0.5 B. 0.75 C. 1 D. 1.25

Suppose three students are selected at random. Let A be the random 
variable representing the number of ABM students that are selected.

16. What is the probability that there will be no ABM student selected?
A. 8/27 B. 4/9 C. 19/27 D. 1

17. What is the probability that at most 2 ABM students are selected? (2 points)
A. 0 B. 0.2222 C. 0.4444 D. 0.9630

18. What is the probability that less than 2 ABM students are selected? (2 points)
A. 0.2222 B. 0.7407 C. 0.9630 D. 1

19. What is the mean of the probability distribution of the random variable A? (2 points)
A. 0.5 B. 0.67 C. 1 D. 1.3

20. What is the variance of the probability distribution of the random variable A? (2 points)
A. 0 B. 0.33 C. 0.44 D. 0.66

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almas8 answered this question
in Statistics·
30 Mar 2022

1. What is the overall level of stress experienced by the senior high school students?
A. 1.1078 B. 1.3333 C. 1.5331 D. 1.9583

2. What is the overall level of stress experienced by CBL students?
A. 1.1078 B. 1.3333 C. 1.5331 D. 1.9583

3. What is the overall level of stress experienced by OBL students?
A. 1.1078 B. 1.3333 C. 1.5331 D. 1.9583

4. What is the standard deviation of the level of stress of the senior high students?
A. 0. 6027 B. 0.7449 C. 0.7494 D. 0.8215

5. What is the median GWA of the CBL students?
A. 85 B. 86 C. 87 D. 89

6. What is the mode of the GWA of the OBL students?
A. 85 B. 86 C. 87 D. 89

7. What is the standard deviation of the GWA of senior high students?
A. 3.39 B. 3.43 C. 3.45 D. 3.68

8. What is the variance of the GWA of STEM students?
A. 11.49 B.11.77 C. 11.90 D. 13.54

9. What generalization can we make about the skewness of the GWA of senior high school students?
A. The data is normally distributed.
B. The data is skewed to the left.
C. The data is skewed to the right.
D. The data is not normally distributed.

10. assuming that the GWA of the senior high school students is normally 
distributed, answer the following questions. 2 point per item.

11. What percent of the senior high school students have GWA below 90? 
A. 0.2843 B. 0.4257 C. 0.5743 D. 0.7157

12. What percent of senior high school students have a GWA above 87? 
A. 0.2944 B. 0.3859 C. 0.6141 D. 0.7056

13. What percent of senior high school students have a grade between 87 and 90? 
A. 0.3298 B. 0.3859 C. 0.6702 D. 0.7157

14. What grade divides the group such that 30% of the students have a grade above 
it? 
A. 85. 01 B. 86.21 C. 88.26 D. 89.81

15. What grade do we find the lowest 10% of the grade? 
A. 80. 26 B. 83.60 C. 90.04 D. 92.44

16. Between what grades contain the middle 50% of the data? 
A. 86-88 B. 86-90 C. 87-88 D. 88-90

17. What percent of ABM students have a grade above 85?
A. 0.1922 B. 0.2148 C. 0.7852 D. 0.8079 

18. What percent of HUMSS students have a grade below 89? 
A. 0.2849 B. 0.3517 C. 0.6103 D. 0.6406

19. What percent of STEM students have a grade between 85 and 89? 
A. 0.1712 B. 0.4160 C. 0.5840 D. 0.5871

20. How many students have a grade between 85 and 89? 
A. 34 B. 76 C. 105 D. 110

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almas8 answered this question
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almas8 answered this question
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almas8 answered this question
in Statistics·
26 Mar 2022

18. Suppose that the vehicle speeds at an interstate location have a normal distribution with a mean equal to 70mph and a standard deviation equal to 8mph. What is the z-score for a speed of 68mph? (2 points)  
A.z=−0.35z=−0.35       B.z=−0.55z=−0.55       C.z=−0.25z=−0.25       D.z=−0.45z=−0.45  19.

The time it takes for Grade 11 students in a certain school to complete a physical fitness test is normally distributed with a mean of 15 minutes and a standard deviation of 4 minutes. If the students who get the fastest 10% completion times will be exempted from the additional gym workout sessions, what is the slowest time for a student to qualify for the exemption? (2 points)

A. 9.88 minutes           B.18.36 minutes          C.8.42 minutes          D.11.64 minutes        

20. Which of the following statements about the normal curve is FALSE?

A.The normal distribution is a continuous random probability distribution.

B. The standard normal distribution is unimodal. 

C. The total area under the normal distribution is one. 

D. All variables that are approximately normally distributed can be transformed into  normal variables.  21. Let z1=−1.80z1=−1.80 and  z2=−0.25z2=−0.25. Which among the following probabilities for z-score illustrates the area under the standard normal curve as shown at the right using  z1z1and z2z2 ?


 

A.P(−1.80<z<−0.25)P(−1.80<z<−0.25)  B.P(z>−0.25)P(z>−0.25)  C.P(−1.80>z<−0.25)P(−1.80>z<−0.25)  D.P(z>−1.80)P(z>−1.80)    22.Terence's scores in Mathematics this semester were rather inconsistent. His scores are as follows: 55, 100, 95, 85, 75, 100. How many scores are within one standard deviation of the mean? (2 points)
A.5     B.6     C.3     D.4 

23. Which is TRUE about the negative z- score?

A. A negative z-score means that the student’s score surpassed more than 50% of his classmates.
B. A negative z-score implies that the students scored higher than the class mean.

C. A negative z-score means that the student’s score is lower than the median. 
D. A negative z-score means that the student’s score is located at the right side of the curve. 

24. Find the area under the standard normal curve between z = 0 and z = – 1.05.
A. 0.1469

B. 0.4332 
C. 0.3531 
D.0.0668

 


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