Module 2 Flashcards
To avoid ______ don’t perform these:
→ phrasing questions neutrally;
→ ensuring that the sampling method is appropriate for the demographic of the target population; and
→ pursuing high response rates.
biased results
If a sample is sufficiently _____ and representative of the ______, the sample statistics, x and s, should be reasonably good estimates of the population parameters, μ and σ, respectively.
large; population
The ___________ has a unique symmetrical shape whose center and width are determined by its mean and standard deviation respectively.
normal distribution
Using the properties of the normal distribution, we can calculate a _________ associated with any range of
values.
probability
Several ________ are helpful for estimating probabilities for a normal distribution.
rules of thumb
About ___ of the probability is contained in the range reaching one standard deviation away from the
mean on either side, that is, P(μ-σ≤ x ≤μ+σ)≈ ____.
68%; 68%
About ____ of the probability is contained in the range reaching two standard deviations (____ to be exact)
away from the mean on either side, that is, P(μ-2σ≤ x ≤μ+2σ)≈ ____.
95%; 1.96; 95%
About ____ of the probability is contained in the range reaching three standard deviations away from the
mean on either side, that is, P(μ-3σ≤ x ≤μ+3σ)≈ ____.
99.7%; 99.7%
A ______ of a point x is the distance x lies from the mean, measured in standard deviations, __ = (x - μ)/σ
z-value; z
The ____________ states that if we take enough sufficiently large samples from any population, the
means of those samples will be normally distributed, regardless of the shape of the underlying population.
Central Limit Theorem
The distribution of those sample’s means, called the _____________, more closely approximates a normal curve as we increase the number of samples and/or the sample size.
Distribution of Sample Means
The ____ of any single sample lies on the normally distributed Distribution of Sample Means, so we can use the _____ curve’s special properties to draw conclusions from a single sample mean.
mean; normal
What is μ?
Population Mean
What is σ?
Population Standard Deviation
What is x-bar?
Sample Mean
What is s?
Sample Standard Deviation.
The mean of the Distribution of Sample Means _____ the mean of the population distribution.
equals
The standard deviation of the Distribution of Sample Means equals the standard deviation of the population distribution divided by the ______ of the sample size. Thus, increasing the sample size ______ the width of the Distribution of Sample Means.
square root; decreases
Using the properties of the normal distribution and the Central Limit Theorem, we can construct a range around the sample mean, called a __________, to estimate the range in which the true ________ mean likely lies.
confidence interval; population
The ____ of the confidence interval depends on the level of confidence, our best estimate of the population standard deviation, and the _____ size. We can only control the level of confidence and the sample size.
width; sample
What is considered a large sample?
n is greater than or equal to 30
For large samples (n≥30), the _____ and ______ bounds are calculated using the following equation: x-bar +or- z(s/SQRT(n))
lower; upper
The function ___________ calculates the margin of error, which we add and subtract from the sample mean to find the confidence interval.
CONFIDENCE.NORM
For _____ samples (n
small
For small samples, we use a __________, which is shorter and wider than a normal distribution.
t-distribution
The t-distribution provides a ____ range, a more conservative estimate of where the true population mean lies.
wider
The function ___________ calculates the margin of error, which we add and subtract from the sample
mean to find the confidence interval.
CONFIDENCE.T
We can also calculate confidence intervals for proportions. To do so, we must convert data to ___________.
dummy (0, 1) variables
When estimating the ___________, we should ensure that the sample size is large enough by checking that both of the following conditions are true: n*p ≥ 5, and n(1−p)≥ 5. If either of these guidelines is not satisfied, we must collect a larger sample.
true population proportion
What is the function for assigning a random ID# between 0 and 1 to each data point?
=RAND()
=NORM.DIST(x, mean, standard_dev, cumulative)
• When cumulative is set to “TRUE”, NORM.DIST finds the ____________, that is, the probability of being less than or equal to the specified value x, for a normal distribution with the specified mean and standard deviation. (Inserting the value _______ provides the height of the normal distribution at the value x, which is not covered in this course.)
cumulative probability; “FALSE”
=NORM.S.DIST(z, cumulative)
• When cumulative is set to “TRUE”, NORM.S.DIST finds the cumulative probability, that is, the probability of being ______ or _____ to the specified value z for a standard normal distribution.
less than or equal
Which function returns the corresponding x-value on a normal distribution for the specified mean, standard deviation, and cumulative probability?
=NORM.INV(probability, mean, standard_dev)
Which function returns the margin of error using a normal distribution for a specified alpha, standard_dev, and size? Alpha is the significance level, which equals one minus the confidence level (for example, a 95% confidence interval would correspond to the significance level 0.05).
=CONFIDENCE.NORM(alpha, standard_dev, size)
Which function returns the margin of error using a t-distribution for a specified alpha, standard_dev, and size?
=CONFIDENCE.T(alpha, standard_dev, size)
Which function returns value_if_true if the specified condition is met, and returns value_if_false if the condition is not met?
=IF(logical_test,[value_if_true],[value_if_false])
Parameters are associated with ________, while Statistics are associated with _______.
Population; Sample
