30 Questions
What is the main goal of estimation in statistics?
To provide a best guess at the population parameter with a calculated degree of error
What distinguishes point estimation from interval estimation?
Point estimation provides a single sample value as an estimate, while interval estimation gives a range of values.
What does it mean for an estimator to be unbiased?
The expectation of the estimator is equal to the population parameter.
In terms of variance, what is expected from a good estimator?
A good estimator should have minimum variance among all estimators.
What property ensures that an estimator approaches the true parameter as sample size increases?
Consistency
Which type of estimation provides a statement of confidence that the interval contains the population parameter value?
Interval estimation
What is the sample mean in the provided text?
32
Which value represents the T table value in the text?
1.833
What is the range for the confidence interval of the mean expenses per family as per the text?
29.038 ≤ μ ≤ 34.962
In what way are the standard error of sampling distribution of sample mean and proportion related to the sample size n?
They are inversely proportional to n
What determines the size of a sample according to the text?
Resources available in terms of time and money
When estimating the population mean with an error not exceeding a fixed value, what should be the relationship between the sample mean and µ ± E?
$ar{x} = µ ± E$
What is a statistical hypothesis?
A claim about an unknown population parameter value
What is the methodology that enables a decision-maker to draw inferences about population characteristics?
Hypothesis testing
In hypothesis testing, what is the statistic used to test a hypothesis called?
Test statistic
What does the level of significance of a test represent?
Probability that observed difference is due to chance
What is the purpose of establishing a critical or rejection region in hypothesis testing?
To decide whether to accept or reject the null hypothesis
What type of test is described by an alternative hypothesis that provides two-sided alternatives to the null hypothesis?
Two-tailed test
What does it mean for an estimator to be efficient?
It has minimum variance among other unbiased estimators
What is the key characteristic of a Uniformly Minimum Variance Unbiased Estimator (UMVUE)?
It is unbiased and has the least variance among other unbiased estimators
For a 95% confidence interval estimate, what is the value of Zc to be used?
1.96
In interval estimation, what does the margin of error represent?
The range within which the parameter is expected to lie
What is crucial for determining the confidence interval estimate of a population parameter?
The sample size
In constructing a confidence interval, what does a higher level of confidence imply?
Higher degree of certainty in the estimate
Which error in hypothesis testing involves rejecting the null hypothesis when it is actually true?
Type I error
In hypothesis testing, what does a right-tailed test compare the population mean to?
Greater than a specific value
What assumption is made when conducting hypothesis testing with large samples (n ≥ 30)?
Normal distribution of the population
When does the Central Limit Theorem not guarantee that the sampling distribution of a sample statistic is normal?
For small sample sizes (less than 30)
What do Type II errors in hypothesis testing refer to?
Error of accepting the null hypothesis when it is false
What do independent random samples drawn from two populations allow in hypothesis testing?
Testing for difference in means between populations
This quiz covers the basics of estimation in statistics, including point estimation and interval estimation. Learn about constructing estimators from sample values and providing the most likely location of a population parameter with a calculated degree of error.
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