STATS SMARTBOOK FOR EXAM 1
A confidence interval narrows if the following is accomplished: Multiple select question.
-the chosen confidence level decreases-the sample size increase
A 95% confidence interval for the population mean is constructed as 6±2. What is the probability of error, α?
0.05
Suppose you are constructing a confidence interval for the mean length of life of AAA batteries. You have the following data: xx=250, n=25, σ=0.5, and zα/2=z0.025=1.96. The margin of error for a 95% confidence interval is closest to: Multiple choice question.
0.2
If α equals 0.05, then the confidence level equals
0.95.
If α equals 0.01, then the confidence level equals
0.99
The confidence level equals
1 - α
AAA batteries are advertised to have a life of about 9 hours of use. With a certain level of confidence, it is advertised that the life is between 8-10 hours. If 9 hours is the point estimate, then the margin of error is
1 hour
A 95% confidence interval for the population mean is constructed as 6±2. What is the margin of error?
2
A sample of size 25 is drawn from a normal population with a population standard deviation of 100. Suppose the mean of the sample is xx = 35. Recall that z0.025=1.96. A 95% confidence interval for the population mean is equal to
35±1.9610025√10025.
If samples of size n are drawn repeatedly from a given population and each sample is used to construct a 95% confidence interval for μ Multiple choice question.
5% of the confidence intervals will fail to contain μ.
What is the confidence level if α = 0.05?
95%
Whenever we construct a confidence interval for the population mean, the margin of error is based upon the standard deviation of xx and the
desired level of confidence
Suppose you are constructing a confidence interval for the population mean. For a given confidence level and sample size, the width of the interval is wider for a
larger standard deviation
The sampling distribution of estimator xx follows a normal distribution when the sample size is large enough. As a rule-of-thumb, we use the following:
n ≥30
In order to construct a confidence interval for μ, the sampling distribution of the estimator xx must follow or approximately follow a(n) ______ distribution.
normal
Regardless of the sample size, the estimator xx follows a normal distribution when the underlying population follows a
normal
The two main components of a confidence interval are the
point estimate and the margin of error
A confidence interval can be interpreted as a
range of values used to estimate an unknown population parameter.
When constructing a confidence interval for the population mean, the factors that affect the width of the confidence interval for a given standard deviation are
the confidence level and the sample size.
The equation for a confidence interval for μ when the value of σ is known is
xx±zα/2σ√nσn.
A 95% confidence interval for the population mean is calculated as [40, 80]. The point estimate for μ is _______. Multiple choice question.
60; Reason: The point estimate is calculated as (40+80)/2=60.
If a 95% confidence interval for μ based on n = 50 has margin of error = 1, what would the margin or error become if you took 200 observations?
.5
The most practical way to reduce the margin of error is by
selecting a larger sample size.
Suppose you are constructing a confidence interval for the population mean. For a given confidence level and standard deviation, the width of the interval is wider for a
smaller sample size
Suppose you wish to construct a 99% confidence interval for μ having margin of error 2 and you know σ = 5.8. How large would your sample size need to be?
56 Reason: n = [(2.575)(5.8)/2]2 = 55.8, round up to 56
A 95% confidence interval for the population mean is constructed as 6±2. What is the point estimate of μ?
6
Suppose you are constructing a confidence interval for the population mean. For a given sample size and population standard deviation, how will the width of the interval change as the confidence level increases?
It gets larger
How is a confidence interval for the mean different from a point estimate of the mean?
The point estimate is the single number xx while a confidence interval is an entire interval of values which is intended to contain μ.
A confidence interval is constructed by using the point estimate as a base, to which we add and subtract the
margin of error
True or False: A confidence interval is constructed around the population mean and makes inference about the sample mean.
False. Reason: A confidence interval is constructed around the sample mean and makes inference about the population mean.
Suppose we wish to derive a confidence interval for the mean of a right-skewed population. In order to derive a valid confidence interval for μ, xx must be based on a sample which
has size n≥30.
Suppose you are constructing a confidence interval for the population mean. For a given sample size and standard deviation, the width of the interval is wider for a
higher confidence level
The confidence level is equal to
100 x (1 - α)%.
Suppose you wish to construct a 95% confidence interval for μ having margin of error 1 and you know σ = 3.2. How large would your sample size need to be?
40