Statistics 1 Final
All estimators are biased since sampling error always exists to some extent
False
In comparing estimators, the more efficient estimator will have a smaller standard error
False
The sample mean is not a random variable when the population parameters are known.
False
Which of the following is not a valid null hypothesis?
H0: μ ≠ 0
Which is an invalid alternative hypothesis?
H1: μ = 18
The efficiency of an estimator depends on the variance of the estimator's sampling distribution
True
The expected value of an unbiased estimator is equal to the parameter whose value is being estimated
True
A sampling distribution describes the distribution of:
a statistic
The Central Limit Theorem (CLT):
applies to any population
The decision rule is
based on the sampling distribution and chosen level of significance
Sampling error can be avoided:
by no method of the statistician's control
A consistent estimator for the mean:
converges on the true parameter as sample size increases
A false positive in a drug test for steroids is a Type II error
false
The Central Limit Theorem says that a histogram of the sample means will have a bell shape, even if the population is skewed and the sample is small
false
The Central Limit Theorem says that, if n exceeds 30, the population will be normal
false
The finite population correction factor (FPCF) can be ignored when the sample size is large relative to the population size.
false
The level of significance refers to the probability of making a Type II error
false
Which is not a step in hypothesis testing?
find the test statistic from the table
The rejection region in a hypothesis test:
is an area in the tail of the sampling distribution
The critical value in a hypothesis test:
is calculated from the sample data
A two-tailed hypothesis test:
is used when the direction of the test is of no interest
Given that in a one-tailed test you cannot reject H0, can you reject H0 in a two-tailed test at the same α?
no
The null hypothesis is:
often a benchmark or historical value
In testing the hypotheses H0: π ≤ π0, H1: π > π0, we would use a:
right tailed test
The level of significance is not:
the chance of accepting a true null hypothesis
The Central Limit Theorem (CLT) implies that:
the distribution of the mean is approximately normal for large n
In the hypothesis H0: μ = μ0, the value of μ0 is not derived from:
the sample
A simultaneous reduction in both α and β will require a larger sample size
true
Assuming that π = .50 is a quick and conservative approach to use in a sample size calculation for a proportion.
true
Compared to using α = .01, choosing α = .001 will make it less likely that a true null hypothesis will be rejected
true
For a mean, we would expect the test statistic to be near zero if the null hypothesis is true
true
If a judge acquits every defendant, the judge will never commit a Type I error. (H0 is the hypothesis of innocence.)
true
In a right-tailed test, the null hypothesis is rejected when the value of the test statistic exceeds the critical value
true
In hypothesis testing, we cannot prove a null hypothesis is true
true
John rejected H0, so we know definitely that he did not commit a Type II error
true
The critical value of a hypothesis test is based on the researcher's selected level of significance
true
The probability of a false positive is decreased if we reduce α
true
The probability of rejecting a true null hypothesis is the significance level of the test
true
When the probability of a Type I error increases, the probability of a Type II error must decrease, ceteris paribus
true
In a statistical test we:
try to reject the null hypothesis