Cheng Zhang

University of Rochester
Tutor

Biography

I was a math tutor at the University of Auckland

Education

BS Physics
University of Rochester

Educator Statistics

Numerade tutor for 4 years
1525 Students Helped

Topics Covered

Unlocking the Power of Functions: Boost Your Programming Skills
Mastering Integration Techniques for Optimal Results
Mastering Partial Derivatives: Essential Techniques and Tips
Exploring the Functions of Multiple Variables

CHENG's Textbook Answer Videos

1

CHENG's Quick Ask Videos

01:19
Intro Stats / AP Statistics

A district sales manager wishes to determine whether there is a difference in mean daily sales volume between two stores in his district. He collects daily sales volume for the month of June to do the analysis. Assume that the population standard deviations are unknown and unequal. The hypothesis test is to be conducted using the 0.01 level of significance. Partial output of his results from Excel can be found in the table below:

Store 1
Store 2
Sample size (n)
30
30
Sample mean daily sales volume (in $1,000)
15
19
Sample standard deviation (in $1,000)
5.2
6.1
Degrees of freedom
56

What is the critical value of the test statistic?
Multiple Choice
±2.667
±2.395
±1.960
−1.645

Cheng Zhang
00:59
Intro Stats / AP Statistics

Acceptance sampling is an important quality control technique, where a batch of data is tested to determine if the proportion of units having a particular attribute exceeds a given percentage. Suppose that 18% of produced items are known to be nonconforming. Every week a batch of items is evaluated and the production machines are adjusted if the proportion of nonconforming items exceeds 24%. [You may find it useful to reference the z table.]

a. What is the probability that the production machines will be adjusted if the batch consists of 84 items? (Round "z" value to 2 decimal places, and final answer to 4 decimal places.)

b. What is the probability that the production machines will be adjusted if the batch consists of 168 items?

Cheng Zhang
02:00
Intro Stats / AP Statistics

The mean serum-creatinine level measured in 12 patients after
they received a newly proposed antibiotic was 1.2 mg/dL.
a. If the mean and standard deviation of serum creatinine in the
general population are 1.0 and 0.4 mg/dL, respectively, then, using
a significance level of 0.05, test if the mean serum-creatinine
level in this group is different from that of the general
population.
b. What is the p-value for this test?
c. Repeat 2a and 2b, but test the hypothesis that the patients
receiving the antibiotic had serum-creatinine levels higher than
(rather than different from, which could imply either higher or
lower) the general population.
d. Repeat 2a and 2b, if the 12 patients receiving the antibiotic
had mean serum creatinine levels of 0.85 and we are testing the
hypothesis that this value is lower than that in the general
population.

Cheng Zhang
01:26
Intro Stats / AP Statistics

1) Select an appropriate point estimate of μ.
Group of answer choices
q
p
s

2) The lower end (lower limit) of a confidence interval is the point estimate minus ________. The upper end (upper limit) of a confidence interval is the point estimate plus ________. Fill in the blanks.
Group of answer choices
standard error
standard deviation
confidence level
margin of error

3) Select all population parameters in the following.
Group of answer choices
σ
s
μ

Cheng Zhang
01:33
Intro Stats / AP Statistics

An important measurement in a textile industry is the
tensile strength of a produced material. Suppose that the tensile
strength (in pounds per square inch) of a roll of woven
polypropylene is normally distributed with a mean of 89 and a
standard deviation of 4.
1) What is the probability that the tensile strength will be
somewhere between 80 and 100 pounds per square inch?
2) Find the probability that the tensile strength of the
woven polypropylene is greater than 95 pounds per square inch
3) Find the two values for tensile strength which give a
middle area between the 80th percentile of the
distribution.

Cheng Zhang
01:11
Intro Stats / AP Statistics

1: Which of the following statements about the formal hypothesis
testing procedure is incorrect?
A.
The null hypothesis must
include a parameter (μ) in its formulation.
B.
The significance
level (α) is the probability of rejecting the null hypothesis when
it is true.
C. The critical value
is computed from sample data to test the null hypothesis.
D.
The decision rule
tells whether to reject or not reject the H0.

Cheng Zhang
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