Question

Q1. The quantitative reasoning scores on the GRE were recorded for students admitted to three different graduate programs as below.

(a): Construct an ANOVA table for the data using Completely Randomized Design?

(b): If you find a significant difference in the average scores for the three programs, Use Tukey’smethod for paired comparisons to determine which means differ significantly. Use α = .05.

Life |
Physical |
Social |

630 |
660 |
440 |

640 |
640 |
330 |

470 |
720 |
670 |

600 |
690 |
570 |

580 |
530 |
590 |

660 |
760 |
540 |

660 |
670 |
4 50 |

480 |
700 |
570 |

650 |
710 |
530 |

710 |
450 |
630 |

Answer #1

Life | Physical | Social | Total | |

Sum | 6080 | 6530 | 5320 | 17930 |

Count | 10 | 10 | 10 | 30 |

Mean, Sum/n | 608 | 653 | 532 | |

Sum of square, Ʃ(xᵢ-x̅)² | 55360 | 79610 | 90960 |

a) Null and Alternative Hypothesis:

Ho: µ1 = µ2 = µ3

H1: At least one mean is different.

Number of treatment, k = 3

Total sample Size, N = 30

df(between) = k-1 = 2

df(within) = N-k = 27

df(total) = N-1 = 29

SS(between) = (Sum1)²/n1 + (Sum2)²/n2 + (Sum3)²/n3 - (Grand Sum)²/ N = 74806.6667

SS(within) = SS1 + SS2 + SS3 = 225930

SS(total) = SS(between) + SS(within) = 300736.6667

MS(between) = SS(between)/df(between) = 37403.3333

MS(within) = SS(within)/df(within) = 8367.7778

F = MS(between)/MS(within) = 4.4699

p-value = F.DIST.RT(4.4699, 2, 27) = 0.0210

Decision:

P-value < α, **Reject** the null hypothesis.

ANOVA | |||||

Source of Variation |
SS |
df |
MS |
F |
P-value |

Between Groups |
74806.6667 |
2 |
37403.3333 |
4.4699 |
0.0210 |

Within Groups |
225930.0000 |
27 |
8367.7778 |
||

Total |
300736.6667 |
29 |

b) At α = 0.05, k = 3, N-K = 27, Q value = 3.51

HSD = 3.51*√(8367.7778/10) = 101.5342

Comparison | Diff. = (xi - xj) | HSD |
Results |

x̅1-x̅2 |
-45 | 101.5342 |
Means are not different |

x̅1-x̅3 |
76 | 101.5342 |
Means are not different |

x̅2-x̅3 |
121 | 101.5342 |
Means are different |

1: Sample:
Gender
Verbal
Math
f
630
660
m
610
550
f
680
660
m
490
390
f
510
520
m
700
700
f
640
710
f
520
470
f
530
500
m
640
570
f
710
700
f
630
520
f
670
580
f
630
610
m
360
290
f
540
490
f
490
560
m
730
760
m
760
700
f
530
670
m
710
700
f
630
610
f
530
490
f
420
410
f
490...

Males
Females
620
660
570
590
540
540
580
560
590
610
580
590
480
610
620
650
570
600
610
620
590
630
570
640
610
590
590
640
570
580
550
560
530
570
560
560
620
600
520
600
560
590
620
590
580
590
610
630
530
560
480
600
590
560
620
560
590
560
580
560
NOTE: use Excel and submit screenshots and directions on how to
do it on excel
These are the...

Create two new columns that separate the analytic GRE scores
into males and females
ID
Gender
Ethnicity
Age
Science Type
Student Status
Verbal GRE
Quantitative GRE
Analytic GRE
College GPA
Graduate GPA
1
Female
White
24
Social
Full Time
450
500
550
3.14
3.42
2
Female
White
25
Social
Full Time
480
580
450
3.11
3.34
3
Female
White
30
Social
Full Time
610
650
680
3.62
3.79
4
Female
White
30
Social
Full Time
540
550
560
3.15
3.46...

Perform a one-sample t-test to determine if the average
quantitative GRE score is significantly lower than 600 (use α =
0.05). Be sure to report the test statistic and
p-value.
ID
Gender
Ethnicity
Age
Science Type
Student Status
Verbal GRE
Quantitative GRE
Analytic GRE
College GPA
Graduate GPA
1
Female
White
24
Social
Full Time
450
500
550
3.14
3.42
2
Female
White
25
Social
Full Time
480
580
450
3.11
3.34
3
Female
White
30
Social
Full Time
610
650...

Estimate: GPA = β0 + β1GRE + ε, where GRE is a student’s score
on the math portion of the Graduate Record Examination (GRE) score
and GPA is the student’s grade point average in graduate
school.
GPA
GRE
3.9
690
3.2
740
3.1
740
2.7
650
2.5
700
2.9
640
2.7
710
2.9
700
2.1
760
2.3
670
3.6
750
2.5
700
3.4
650
3.9
690
3.3
700
2.7
680
3.8
660
2.6
660
3.9
710
3.8
760
3
690...

Males
Females
620
660
570
590
540
540
580
560
590
610
580
590
480
610
620
650
570
600
610
620
590
630
570
640
610
590
590
640
570
580
550
560
530
570
560
560
620
600
520
600
560
590
620
590
580
590
610
630
530
560
480
600
590
560
620
560
590
560
580
560
1. Summarize the data visually. This will require referencing
chapter 2 and determining the best way to visually...

Use the data for two Sydney suburbs to answer questions
1-5:
1 Using Excel or other appropriate
software, produce two separate histograms for the median rental
prices of the two selected suburbs, respectively.
Use an appropriate number
of bins for your histogram and remember to label the axes. Describe
and compare the two histograms, including the central location,
dispersion and skewness. [1 mark]
2 Compute the sample means and sample
standard deviations of the median rental prices...

Let's say you want to test (at 0.05 significance level) whether
female students, on average, scores more than 600 on the verbal SAT
exam. 20 female students were selected randomly and their scores
(such as in the table): 650 730 510 670 480 800 690 530 590 620 710
670 640 780 650 490 800 600 510 700
a) Suppose σ = 100. Calculate the test statistic value is
used.
b) Suppose σ is unknown. Calculate the test statistic value...

Three admission test preparation programs are being evaluated.
Suppose the scores obtained by a sample of 20 people who used the
programs provided the following data.
Program
A
B
C
530
450
600
400
530
640
470
400
590
540
420
470
470
490
570
620
380
610
550
580
Find the value of the test statistic. (Round your answer to two
decimal places.)
Find the p-value. (Round your answer to three decimal
places.)
p-value =
Forty-minute workouts of one...

Three admission test preparation programs are being evaluated.
Suppose the scores obtained by a sample of 20 people who used the
programs provided the following data.
Program
A
B
C
510
450
600
400
510
620
470
400
560
520
430
470
470
460
570
630
390
640
550
590
Use the Kruskal-Wallis test to determine whether there is a
significant difference among the three test preparation programs.
Use α = 0.05.
Find the p-value. (Round your answer to three...

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