MGSC EXAM 4
a confidence interval narrows if the following is accomplished:
-the chosen confidence level decreases -the sample size increase
we can reject the null hypothesis when the
p-value < α
the parameter P represents the
population proportion
when estimating the population mean, the Tdf distribution is used when the..
population variance is unknown
a confidence interval can be interpreted as a
range of values used to estimate an unknown population parameter
A 95% confidence interval for µ implies that if numerous samples are taken from a population, 95% of the intervals will contain µ.
true
the optimal values of type 1 and type 11 errors require a compromise in balancing the costs of each type of error
true
A t distribution ..
has slightly broader tails than the z distribution
a binomial distribution can be approximated by a _______ distribution for large sample sizes
normal
the p-value is calculated assuming the
null hypothesis is true
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 - increases the margin of error-> wider interval
For a given sample size η ________________.
decreasing the probability of a Type I error α will increase the probability of a Type II error β
A type 11 error occurs when we
do not reject the null hypothesis when it is actually false
in order to construct a confidence interval for µ, the sampling distribution of the estimator x̅ must follow a ______________ distribution
normal
the sampling distribution of the estimator x̅ follows a normal distribution when the underlying population follows a __________ distribution
normal
when the sample size is sufficiently large, we can approximate the sampling distribution of the sample proportion using the ....
normal distribution
when preforming a hypothesis test on µ, the p-value is defined as the
observed probability of making a type 1 error
if the sample data provides significant evidence that the null hypothesis is incorrect, then we
reject the null hypothesis
A type 1 error occurs when we
reject the null hypothesis when it is actually true
In hypothesis testing, two correct decisions are possible:
rejecting the null hypothesis when the null hypothesis is false & not rejecting the null hypothesis when it is true
the critical value approach specifies a region of values, called the_______, if the test statistic falls in this region, we reject the_____.
rejection region, null hypothesis
the_________ p̂ is used as the point estimator for the _______ p
sample proportion, population proportion
In inferential statistics, we use_____ information to make inferences about an unknown______ paramter
sample, population
When constructing a confidence interval for the population mean, the factors the affect the width of the confidence interval for a given standard deviation are...
the confidence level and the sample size
As a general guideline, we use the alternative hypothesis as a vehicle to establish something new, or contest the status quo, for which a corrective action may be required.
true
Steps in the p-value approach to hypothesis testing-
1. specify the null and alternative hypothesis 2. specify the significance level 3. calculate the value of the test statistic and its p-value 4. state the conclusion and interpret results
the null hypothesis for a two sided hypothesis test for a population mean would be denoted as
Ho: µ=µo
the significance level is the probability of making
a type 1 error
For a given sample size n, α can only be reduced
at the expense of increasing β
what is NOT a step we use when formulating the null and alternative hypotheses?
calculate the value of the sample statistic
the standard error of the sample mean is NOT affected by the
confidence level
the two equivalent methods to solve a hypothesis test are the
critical value approach and the p-value approach
the most practical way to reduce the margin of error is to_____________
increase the sample size
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
Alpha (α) is often referred to as the
level of significance
precision in interval estimates is implied by a ____ margin of error
low
a confidence interval is constructed by using the point estimate as a base, to which we add and subtract the
margin of error
If the null hypothesis is rejected at a 1% significance level, then _____________.
the null hypothesis will be rejected at a 5% significance level