Hamzah Choudary

Princeton University
STEM Student

Biography

Dedicated Numerade tutor, specializing in making math accessible and enjoyable. From arithmetic to advanced calculus, I empower students to see the elegance and practicality in mathematical thinking.

Education

BS Mathematics
Princeton University

Educator Statistics

Numerade tutor for 3 years
200 Students Helped

Topics Covered

Master the Fundamentals of Physics: Learn Physics Basics

Hamzah's Textbook Answer Videos

1

Hamzah's Quick Ask Videos

02:59
Intro Stats / AP Statistics

A real estate developer is considering investing in a shopping
mall on the outskirts of Toledo, Ohio. Three parcels of land are
being considered. Of particular concern is the income in the area
surrounding the new mall. A random sample of four families is
selected near each proposed site. At the 0.05 level of
significance, can the developer conclude there is a difference in
the mean incomes? Run the ANOVA Global and Post Hoc tests. What
Bonferonni alpha should be used when conducting Post Hoc tests? A.
0.0033 B. 0.0083 C. 0.0167 D. 0.0001?
Southwick Area
Franklin Area
Orchard Area
64
74
75
68
71
80
70
69
76
60
70
78

Hamzah Choudary
02:48
Intro Stats / AP Statistics

Interval #
1
2
3
4
5
6
7
8
9
10
Observer 1
X
0
X
X
X
0
X
0
0
X
Observer 2
X
0
0
X
X
X
X
0
0
X
Using the data in the table above, calculate inter-observer
agreement (IOA) using 3 different formulas. X = Behavior occurred,
0 = Behavior did not occur.
1. Formula for Interval-by-Interval IOA = # of intervals both
observers are in agreement/total # of intervals x 100
2. Formula for Scored Interval IOA = # of intervals both
observers recorded occurrence of behavior/total # of intervals at
least one observer recorded occurrence of behavior x 100
3. Formula for Unscored Interval IOA = # of intervals both
observers recorded non-occurrence of behavior/total # of intervals
at least one observer recorded non-occurrence of behavior x 100

Hamzah Choudary
01:19
Intro Stats / AP Statistics

Consider a regression model estimated with a very simple data
set.
There are only two observations and one explanatory variable,
with no intercept term.
The observations are:
y = (4, 3) and x = (1, 0)
The slope coefficient on x , beta-hat, is 4. (Why? Consider the
residuals.)
Calculate the R-squared for this regression.
(Notice that, in this special case, we will not subtracting
Y-bar in the calculation of TSS, since the intercept is not in the
model.)

Hamzah Choudary
01:22
Intro Stats / AP Statistics

To test whether the mean time needed to mix a batch of material
is the same for machines produced by three manufacturers, a
chemical company obtained the following data on the time (in
minutes) needed to mix the material.
Manufacturer
1
2
3
20
29
20
26
25
18
23
32
23
27
30
27
1. Use these data to test whether the population mean times for
mixing a batch of material differ for the three manufacturers.
Use
α = 0.05.
State the null and alternative hypotheses.
A.
H0: μ1 = μ2 = μ3

Ha: μ1 ≠ μ2 ≠ μ3H0:
B. At least two of the population means are equal.
Ha: At least two of the
population means are different.
C.
H0: μ1 = μ2 = μ3
Ha: Not all the population
means are equal
D.
H0: μ1 ≠ μ2 ≠ μ3

Ha: μ1 = μ2 = μ3H0:
E. Not all the population means are equal.

Ha: μ1 = μ2 = μ3
2. Find the value of the test statistic. (Round your answer to
two decimal places.)
3. Find the p-value. (Round your answer to three
decimal places.)
p-value =
4. State your conclusion.
A. Reject H0. There is not sufficient
evidence to conclude that the mean time needed to mix a batch of
material is not the same for each manufacturer.
B. Do not reject H0. There is not
sufficient evidence to conclude that the mean time needed to mix a
batch of material is not the same for each
manufacturer.
C. Do not reject H0. There is
sufficient evidence to conclude that the mean time needed to mix a
batch of material is not the same for each manufacturer.
D. Reject H0. There is sufficient
evidence to conclude that the mean time needed to mix a batch of
material is not the same for each manufacturer.
5. At the α = 0.05 level of significance, use Fisher's
LSD procedure to test for the equality of the means for
manufacturers 1 and 3.
A. Find the value of LSD. (Round your answer to two decimal
places.)
LSD =
B. Find the pairwise absolute difference between sample means
for manufacturers 1 and 3.
What conclusion can you draw after carrying out this test?
x1 − x3
C. A. There is a significant difference between the means for
manufacturer 1 and manufacturer 3.
B. There is not a significant difference
between the means for manufacturer 1 and manufacturer
3.

Hamzah Choudary
01:18
Intro Stats / AP Statistics

The Chinese Mini Mental Status Test (CMMS) is a 114-item test that aims to identify people with Alzheimer's and senile dementia in China.

CMMS score
No Dementia
Dementia
0-5
0
2
6-10
0
1
11-15
3
4
16-20
9
5
21-25
16
3
26-30
18
1
Total
46
16

Suppose that a cutoff point in the test is established to identify the test with Dementia. Determine:
a) the sensitivity of the test
b) the specificity of the test

Suppose possible cutoff points are considered ()
c) Construct the corresponding ROC Curve.
d) Estimate and interpret the corresponding AUC

Hamzah Choudary
01:58
Intro Stats / AP Statistics

Refer to the data set in the accompanying table. Assume that the
paired sample data is a simple random sample and the differences
have a distribution that is approximately normal. Use a
significance level of 0.10 to test for a difference between the
weights of discarded paper (in pounds) and weights of
discarded plastic (in pounds).
In this example,μd is the mean value of the differences d
for the population of all pairs of data, where each
individual difference d is defined as the weight of discarded paper
minus the weight of discarded plastic for a household. What are the
null and alternative hypotheses for the hypothesis test?
What is the t statistic.
What is the P Value
Household Paper
Plastic
1 6.44 8.40
2 9.41 3.36
3 6.67 6.09
4 6.05 2.73
5 11.08 12.47
6 8.72 9.20
7 9.19 3.74
8 6.98 2.65
9 6.16 5.88
10 17.65 11.26
11 6.33 3.86
12 7.98 6.09
13 11.36 10.25
14 9.83 6.26
15 12.73 14.83
16 2.41 1.13
17 13.05 12.31
18 12.43 8.57
19 8.82 11.89
20 5.86 3.91
21 6.38 8.82
22 7.57 5.92
23 2.80 5.92
24 3.27 0.63
25 13.31 19.70
26 6.83 3.57
27 9.45 3.02
28 15.09 9.11
29 13.61 8.95
30 16.08 14.36

Hamzah Choudary
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