Statistics Unit Eight Review

Questions and Answers

Have all conditions for inference been met for the director estimating resting heart rate?

False

What is a correct interpretation of the 95 percent confidence level based on the average of alfalfa weevils?

If we repeatedly sampled this field, taking samples of 80 plants and constructing 95% confidence intervals, then approximately 95 percent of these intervals would include the population mean number of alfalfa weevils on an alfalfa plant in this field.

What is the most appropriate interval for the manager estimating subscriber approval of a new cover format?

A two-sample z-interval for a population proportion

A one-sample z-interval for a population proportion (correct)

A one-sample t-interval for a population mean

A paired sample t-interval

What is the best interpretation of the 95 percent confidence level based on the polling agency's survey?

We would expect about 95 of the 100 confidence intervals to contain the proportion of all citizens of the United States who are optimistic about the economy. Signup and view all the answers

What must be true regarding the probability that the confidence interval includes the population proportion for community service participants?

The probability that the confidence interval will include the population proportion is 0.99. Signup and view all the answers

Why must the population size be at least 10 times the sample size when using a one-sample t-procedure?

To ensure that the degree of dependence among observations is negligible. Signup and view all the answers

Which condition is not needed for the inference when estimating caffeine content in coffee?

The graph of the sample data is symmetric with no outliers. Signup and view all the answers

What is a 98 percent confidence interval for the proportion of students writing their name on their USB drive?

0.6±2.33300(0.4)(0.6) Signup and view all the answers

What is a correct interpretation of the 95 percent confidence level based on monthly rent?

In repeated sampling, the method produces intervals that include the population mean approximately 95 percent of the time. Signup and view all the answers

Study Notes

Confidence Intervals and Conditions for Inference

Non-random sample selection can invalidate inference; example: a corporate fitness director studied employees with activity trackers.
A 95% confidence interval reflects that approximately 95% of intervals constructed from repeated samples will capture the true population mean; based on study of alfalfa weevils showing an average of 2.5.

Estimating Population Proportions

A one-sample z-interval is appropriate for estimating proportions, as in the case of a magazine manager wanting to gauge subscriber approval of a new cover.
Polling agencies create confidence intervals, expecting about 95 out of 100 constructed intervals to encompass citizens' optimism about the economy.

Understanding Confidence Levels

A 99% confidence level indicates a 99% probability that a constructed confidence interval includes the true population proportion; relevant for community service participation in schools.
Conditions for one-sample t-procedures include a population size being at least 10 times the sample size to maintain negligible dependence among observations.

Sample Data Specifics

Sample data symmetry and outlier presence don't always determine inference conditions, e.g., caffeine levels in coffee exhibited right skew and an outlier.
For a computer classroom study, a 98% confidence interval for students who label their USB drives can be calculated, showcasing practical application of proportions.

Interpretations of Confidence Intervals

A confidence interval's reliability is illustrated in rent studies: a sample mean of $820 with a 95% confidence interval suggests that repeated sampling can include the true mean approximately 95% of the time.

Description

Test your knowledge with this review quiz on Statistics Unit Eight. Focus on understanding confidence intervals and sampling methods through various scenarios and questions. Perfect for preparing for your final exam in statistics!