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Math
Statistics
Statistics Final Exam
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Terms in this set (72)
shape of uniform distribution
rectangle
shape of normal distribution
bell shaped
A normal distribution is symmetric about a vertical axis through its means
True
Standard deviation (o) of the standard normal distribution
1
Population mean (u) of the standard normal distribution
0
Percentage of observations that lie within 1 standard deviation of mean
68%
Percentage of observations that lie within 2 standard deviations of mean
95%
Percentage of observations that lie within 3 standard deviations of mean
99%
Convert a probability about any normal random variable X to a probability about a standard normal random variable Z using...
a z-score
P(X>x) is the same as P(Z>z) when z is the corresponding z-score
True
What is the area under any normal curve?
1
X normal distribution
Use Z=X-u/o
Sampling distribution of sample mean
a probability distribution of all possible sample means of a given sample size
Sampling distribution of X
the distribution of all x 's from all possible samples.
If the population is known to have a normal distribution, then the sampling distribution must be normal
True
When we do not know the if the population has a normal distribution, the CLT says that the sampling distribution is approximately normally distributed when...
the sample size is sufficiently large
When the population has a normal distribution, the expected mean of the sampling distribution...
is equal to the true mean
Just like the sample mean, the sample variance takes on different values depending on the particular sample you take, and therefore, the sample variance has a sampling distribution
True
The Chi-Square distribution is symmetrical
False
Variance of a constant
Zero
What does not impact the width of a confidence interval?
The point estimate
What does impact the width of a confidence interval?
sample size, standard deviation, and choice of confidence interval
Chi-Square Distribution
A sum of squares of a random normal variable
Consequence of accepting the alternative hypothesis
The conjecture has not been supported by the observed statistic
Sampling distribution for the variance of a Uniform random variable
does not approximate a normal distribution for sample sizes exceeding 1000
The t-distribution is symmetric with less area in the tail regions compared to the Standard Normal Distribution when n<120
False
When do we use the t-distribution?
When the population variance or standard deviation is unknown
When do we use the Z-test?
When the population variance or standard deviation is known
Type I Error (a)
Rejecting the null when Ho is true
Type II Error (B)
Accepting the null when Ho is false
A given confidence interval for the mean is centered at...
The population mean (u)
Which distribution do you use to find critical values for confidence intervals (n=20) of a mean when the population standard deviation is unknown
t-distribution
A 99% confidence interval has a larger margin of error than the corresponding 95% confidence interval
True
A confidence interval is a range of reasonable values for a...
population parameter
When population variances are known, which distribution do we use for finding the critical value when constructing a confidence interval for the population man (u)?
normal distribution
Independent two-samples t-test
average # of sleep per night in hours for 4th vs. 8th
Paired t-test
ask same group over a period of time
In a hypothesis test the resulting p-value is 0.043. This means that we can find statistical significance at:
The 0.05 but not at the 0.01 level
Population proportion p is a...
Parameter
If the null hypothesis is actually false, which of these statements characterizes the situation where the value of the test statistic falls in the rejection region?
The correct decision of rejecting the null hypothesis will be made
When the confidence level increases...
the width of the confidence interval increases
Variance (o2) of a binomial proportion
npq
Sample proportion (p-hat) is a...
Statistic
When the sample size n is large, a confidence interval for p can be constructed using the...
normal distribution
When constructing a confidence interval for population proportion p, what does "large n" indicate?
n times p-hat is greater than or equal to 5 and n times q-hat is greater than or equal to 5
When we do a hypothesis test, we are testing a claim about a...
Population parameter
For a single sample t-test against a specified reference mean, the degrees of freedom are used to compute the sample mean (x)
False
The level of significance (a) or Type I Error is selected by the investigator on the basis of...
expected losses from a Type I error
Statistical significance necessarily implies...
a suitable sample size was used to detect a difference large enough to be considered unlikely under the null hypothesis
p-value is less than a
Reject null
p-value is greater than a
Accept null
If every observation is multiplied by 2, then the t-statistic if multiplied by 2
False
Has a mean of zero and its shape depends on degrees of freedome
t-distribution
"equal to"
null hypothesis
"greater than"
alternative hypothesis
If your alt hypothesis has "greater than" in it, then the area under the curve greater (to the right) than your test statistic is equal to the p-value
True
If we do not reject the null hypothesis...
we do not have evidence to say the alternative hypothesis is true
Doing an independent samples t-test, do not know population standard deviations, cannot assume the population standard deviations are equal
Unpooled standard deviation case
Alternative hypothesis
One-tailed test vs two-tailed test
Do a hypothesis test about a proportion p and have a small sample
Binomial
Do a hypothesis test about a proportion p and have a large sample
either the normal or binomial distributions
We can use Analysis of Variance to compare 3 or more groups proportions where each independent group has n=5 measurements
False
Chi-squared goodness of fit test
Used to determine if a population has a specified theoretical distribution
Chi-squared test of independence null hypothesis
two categorical variables are independent in the population
Chi-squared test of homogeneity
Used to compare the observed for data one categorical variable with two or more groups against a proposed probability distribution
When finding the p-value using a chi-squared test statistic...
the p-value is always the area to the RIGHT of the test statistic under the chi-squared curve
Outliers do not bias the least-squares regression line
False
In the context of linear regression, extrapolation is...
not recommended to predict values of Y for values of X that were not part of the regression model
A least squares regression line always passes through Y and X of the data values
True
Analysis of Variance is a method that is used to identify differences among more than 2 groups means
True
Monte Carlo simulation is a computer intensive technique that can be used to study the behavior of any sampling distribution for selected sample sizes and is a useful tool to demonstrate the Central Limit Theorem
True
The t-distribution essentially converges to the Normal distribution for sample sizes of 120. The tail regions of the t-distribution converge more slowly with increasing n relative to center of the distribution.
True
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