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TEST 3 Review
TEST 3 Review
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1
· The standard deviation of the sampling distribution is also known as the-------
Median
Variance
Standard error
Standard Deviation
2
In a 2004 Gallup Poll, 70% of U.S. adults support the death penalty. If we sample 750 adults, what is the mean & SD ?
μX= 525, σX= 157.5
μX= 12.55, σX= 525
μX= 525, σX= 12.55
μX= 525, σX= 125.5
3
Find critical Z at confidence level 99%
Z_c\approx1.645
Z_c\approx2.576
Z_c\approx1.64
Z_c\approx1.96
4
You observe the sex of the next 20 children born at a local hospital: X is the number of girls among them.
Binomial
Not Binomial
5
Given: n = 6, p = 0.42, find P(x ≥ 1) round to 5 dp
0.91
0.96
0.96193
0.9619
6
The Binomial probability a collection of all of probabilities for each x. to find probability for a particular x value,
none
cdf
pdf
both
7
What happens to the standard deviation and margin of error as the sample size (n) increases?
Larger sample sizes typically reduce variability
A larger sample size generally reduces the margin of error
Larger sample sizes yield more reliable estimate
Increasing sample size does impact these values
8
The distributions of -------- means are more normal that the distributions of individual observations
Distribution
Sample
Variance
Population
9
foot length of a randomly chosen male is normal random variable with a mean 11 and SD 1.5. The probability is 0.4
=NORM.INV(AREA,MEAN,STANDARD DEVIATION,1)
=NORM.DIST(X,MEAN,STANDARD DEVIATION, TRUE)
=NORM.DIST(X,MEAN,STANDARD DEVIATION, FALSE)
=NORM.INV(AREA,MEAN,STANDARD DEVIATION)
10
· In the normal distribution with mean and standard deviation :
99.7% of the observations fall within 3SD
95% of the observations fall within 1SD
99% of the observations fall within 1SD
68% of the observations fall within 1SD
11
Given n = 12, p = 0.65 find P(x ≤ 8) round to 4 decimal places.
0.65
0.6533
0.653347
0.65334
12
If we randomly sample 120 people, we expect 12 to have blood type B. What is standard deviation of number? hint : p=x/n
σ=\sqrt{n.p.\left(1-p\right)} , σ = 10.8
σ=\sqrt{n.p.\left(1-p\right)} , σ = 3
σ=\sqrt{n.p.\left(1-p\right)} , σ = 3.29
σ=\sqrt{n.p.\left(1-p\right)} , σ = 10.00
13
A number that describes the population. Usually unknown in real statistical practice.
Random sample
SRS
Statistics
Population
14
Follow a normal distribution, with a mean of $27 and a standard deviation of $4. Tom earns $22.50 an hour. His z-score:
-1.125
22.50
1.125
-4.50
15
Variables are represented by values that are typically measurements, the variable can take any value within interval.
Both
Discrete Random Variable
Continuous Random Variable
none
16
For any continuous distribution
P\left(X<2\right)\ne P\left(X\ge2\right)
P\left(X<2\right)=P\left(X\le2\right)
P\left(X\le2\right)\ne P\left(X\ge2\right)
P\left(X<2\right)\ne P\left(X\le2\right)
17
If we randomly sample 120 people, we expect 12 to have blood type B. What is standard deviation of number? hint : p=x/n
σ=\sqrt{n.p.\left(1-p\right)} , σ = 3.29
σ=\sqrt{n.p.\left(1-p\right)} , σ = 10.8
σ=\sqrt{n.p.\left(1-p\right)} , σ = 3
σ=\sqrt{n.p.\left(1-p\right)} , σ = 10.00
18
The ... is the distribution of values taken by the statistic in all possible samples of same size from same population
standard distribution
Population distribution
sampling distribution
Probability distribution
19
In a Binomial setting, we can use a normal approximation if
np >10
n(1-p) > 10
np >10 , n(1-p) > 10
np >10 , n(1-p) >= 10
20
Finding Normal Probabilities without z-scores
P\left(X\ge a\right)=NORM.DIST\left(a,μ,σ,1\right)
P\left(X\le b\right)=NORM.DIST\left(b,μ,σ,1\right)
P\left(X\ge a\right)=1-NORM.DIST\left(a,μ,σ,1\right)
P\left(X\le b\right)=1-NORM.DIST\left(b,μ,σ,1\right)
21
· Gives a measure of the relative position of a single observation within a distribution based on the mean and SD
Z- score
Quartile
Standard Deviation
Mode
22
What does it mean when the confidence level (C) increases in relation to the z-score and margin of error?
The confidence level has no effect on the MOE or interval width.
The margin of error decreases, making intervals narrower and more precise.
The margin of error stays constant regardless of changes in C or z.
C increase, z increases, MOE increase ,intervals be wider, less precision
23
72% of women have never been married rounding to 4 dp. if 15 women are selected at least 13 of them have been married
0.0000
0.00
3.7640
3.74095E-06
24
There are 6 members in a family (2 parents and 4 children). Let X be the number of family members who have blue eyes.
Not Binomial
BOTH
Binomial
None
25
Which interpretation accurately describes a z-score?
number of standard deviations that an observation is away from mean + or -
A z-score shows the range of values in a dataset.
A z-score measures the average value of a dataset.
A z-score indicates the total number of observations in a dataset.
26
What term is used in statistics to indicate the value below which a given percentage of observations in a group falls?
Mode
Quartile
Mean
Percentile
27
Rewriting Inequalities So You Can Use Excel P(x ≥ k) =
P(x < k – 1)
1 – P(x ≤ k)
P(x ≤ k – 1)
1 – P(x ≤ k – 1)
28
·The standard deviation gets smaller as n gets ???
lower
larger
smaller
equal
29
A special type of random variable is called a binomial random variable.
Continuous random variable
discrete random variable
simple random variable
random variable
