Exam #2 - Chapters 5 - 10 Flashcards
What is a parameter and what variables are associated with its mean, variance, and standard deviation?
A numerical descriptive that measures a population and is a fixed numerical value
Mean - μ
Variance - σ^2
Standard Deviation - σ
What is a statistic and what variables are associated with its mean, variance, and standard deviation?
A numerical descriptive that measures a sample (subset of a population) and is a changing numerical value with a distribution that is large and random
Mean - x̄
Variance - s^2
Standard Deviation - s
What is an estimation?
Estimation of the values of a population parameter
Symbol: x̄
What is testing?
Formulation of a decision about the value of a population parameter
What is regression?
Predictions about the value of a statistical variable
What is the Central Limit Theorem and what does it guarantee?
A theory about the sample distribution of x̄.
Guarantees:
- The distribution of x̄ given x is normal.
- The distribution of x̄ given x follows any distribution.
When x is a random variable with a normal distribution, what is true?
1) The x̄ distribution is a normal distribution.
2) The mean of the x̄ distribution is μ˯x̄ (mean for population).
3) The standard deviation of the x̄ distribution is σ˯x̄ = σ/√(n)
In a standard normal distribution, what happens when you increase the value of “n”?
The value of the standard error gets smaller
When x is a random variable with any distribution, what is true?
1) Given that x follow any distribution, the value of “n” is greater or equal to 30.
2) The sampling distribution of x̄ is approximately normal
3) The mean and standard deviation are the same as when a normal distribution is present.
- μ˯x̄
- σ˯x̄ = σ/√(n)
What are the three inference methods?
1) Estimation
2) Hypothesis Testing
3) Regression
When you have a random variable with a fixed population parameter, which symbol do you use to show this value?
μ
When you have a random variable with a random sample statistic, which symbol do you use to show this value?
x̄
What is a point estimate?
An estimate of the parameter using a single number
- “x̄ is the point estimate for μ” but they are not exactly the same values
What is a margin of error?
The difference between the sample point estimate and the true population parameter.
- | x̄ - μ |
- Large value = x̄ not accurate; Small value = x̄ pretty accurate
With respect to the confidence level, what is the critical value?
A number that the area under the standard normal curve between -z˯c and z˯c equals c.
- c = P(-z˯c < x < z˯c)
What is the equation for the maximal margin of error?
E = (z˯c · σ) / √(n)
What is the confidence interval for μ?
(x̄ - E, x̄ + E)
- (x̄ - E < μ < x̄ + E)
How do we write an interpretation statement for a confidence interval?
We are __% confident that the interval calculated contains the population mean μ.
With respect to “n”, what should you do if you get a number with at least one decimal place?
Always round up to the nearest whole number
What is the equation to use when the sample statistic s is used to approximate population parameter σ?
t = (x̄ - μ) / (s / √(n))
NOT NORMALLY DISTRIBUTED
What is a degree of freedom and how does it relate to this equation:
t = (x̄ - μ) / (s / √(n))
Uses Student’s t distribution
- degree of freedom = n - 1
- used to find t˯c
What is the shape of the Student’s t distribution?
Mound-shaped and symmetric
The Student’s t distribution are symmetric are what value of t?
t = 0
As the degrees of freedom increase, what distribution does the Student’s t distribution become more like?
It becomes more like the standard normal curve
What is the equation used to find the confidence interval using sample standard deviation?
E = (t˯c · s) / √(n)
USE WHEN σ IS UNKNOWN
What are the characteristics of an independent sample?
Subjects are split randomly:
- treatment
- placebo
ALLOWS COMPARISON OF MEANS BETWEEN TWO DIFFERENT GROUPS
What are the characteristics of a dependent sample?
1) Subjects all go through the same pre-test
2) Subjects go through a training session
3) Subjects all go through the same post-test
What do we require of both n values when both x values are not normal?
Both n values must be greater or equal to 30.
What is the equation for standard deviation when the μ values are unknown?
Standard Deviation = √( (σ˯1^2/n˯1) + (σ˯2^2/n˯2) )
What is the equation for standard deviation when the σ values are unknown?
Standard Deviation = √( (S˯1^2/n˯1) + (S˯2^2/n˯2) )
What is the equation for the confidence interval when both values of σ are known?
Confidence Interval: [ (x̄˯1 - x̄˯2) - E, (x̄˯1 - x̄˯2) + E) ]
E = z˯c · √( (σ˯1^2/n˯1) + (σ˯2^2/n˯2) )
What is the equation for the confidence interval when both values of σ are unknown?
Confidence Interval: [ (x̄˯1 - x̄˯2) - E, (x̄˯1 - x̄˯2) + E) ]
E = t˯c · √( (σ˯1^2/n˯1) + (σ˯2^2/n˯2) )
- use small n value when calculating the df to find t˯c
What is a Null Hypothesis and how would would state it?
A given value of a production or specification
H˯0: μ = (given)
What are the three different versions of alternative hypotheses?
H˯1: μ ≠ (given)
H˯2: μ < (given)
H˯3: μ > (given)
How would an alternative hypothesis of H˯1: μ ≠ (given) be skewed?
two-tailed
How would an alternative hypothesis of H˯2: μ < (given) be skewed?
left-tailed
How would an alternative hypothesis of H˯2: μ > (given) be skewed?
right-tailed
State the alternative hypothesis if you have no information regarding how the population mean might differ from the
claimed population mean.
H˯1: μ ≠ (given)
State the alternative hypothesis if you believe the population mean may be greater than the claimed population mean.
H˯2: μ > (given)
State the alternative hypothesis if you believe the population mean may be less than the claimed population mean.
H˯3: μ < (given)
