Proportions
A population p is 0.40. In a sample of n=100, what is the mean of the sampling distribution?
a. 0.40
b.40
c. 0.04
d. 0.60
a. 0.40
As n increases, the standard deviation of the sampling distribution...
A) Increases
B) Stays the same
C) Decreases
D) Becomes standard deviation
C. Decreases
The "10% Condition" is used to check for:
A) Normality
B) Independence
C) Bias
D) Mean alignment
B. Independence
A value describing a population is a:
A) Statistic
B) Sample
C) Parameter
D) Estimate
C. Parameter
Which is the correct formula for the standard deviation of p^
a)np(1-p))
b) Square root np(1-p)
c) Square root p(1-p)/n
d standard deviation/square root of n
C square root p(1-p)/n
population mean=50, standard deviation 10
if n=25, standard deviation x bar is
a)10
b)2
c)0.4
d)2.5
for the normal approximation of p^ we check
a) n>_ 30
b)np>_10, nq >_ 10
c) standard deviation is known
d) population is normal
Which law says as x bar increases to the population mean as n grows
a) Central Limit Theorem
b) Law of Large Numbers
c) Rule of three
d) Law of averages
b) law of large numbers
A sample size is quadrupled. How does the standard deviation of the proportion change?
a. It is cut in half
b. It is doubled
c. It is divided by 4
d. It remains unchanged
A. It is cut in half
a population has standard deviation=15, to get standard deviation of x-bar what n is needed
a) n=5
b) n=25
c) n=45
d) n=225
b) n=25
Why must the population be at least 10n when calculating the standard deviation of a sampling distribution?
We check this to ensure independence. When sampling without replacement from a finite population, the 10% rule allows us to use the standard deviation formula as if the selections were independent.
Define a "sampling distribution" in your own words.
A sampling distribution is the distribution of values taken by a statistic in all possible samples of the same size n from the same population.
If 30% of a population has a certain trait, and you take a sample of n = 100:
How many "successes" do you expect to see?
If you expect 30 successes and 70 failures, is the sample size big enough to use a Normal curve?
1) 30 successes
2) Yes, because both successes (30) and failures (70) equal at least 10
You take a sample of 5 people from a population that is very skewed. Can you use a Normal curve to find probabilities for the sample mean? Why or why not?
No, The sample is too small (n=5), for a skewed population you need a larger sample.
If you want to use the Normal distribution for a sample mean x bar, what is the "magic number" your sample size n should usually reach?
n>_ 30
Imagine you take 100 different samples and calculate the mean for each one. If you graph all those 100 means, what do we call that specific type of graph?
A sampling distribution.
If you double your sample size, does your estimate become more accurate or less accurate?
More accurate, Larger samples have less "spread", so the results are more consistent.
A population has a mean of 100. If you take a sample of 50 people, what would you expect the mean of your sampling distribution to be?
he mean of the sampling distribution is the same as the population mean.
The Central Limit Theorem (CLT) says that as you collect more data, the shape of the sample means looks more and more like a specific shape. What is that shape?
The Normal Distribution
If a scale always adds 5 pounds to everyone's actual weight, is that scale biased or just variable?
It is biased. Bias means the "center" of your data is consistently off-target in one direction.