Chapter 10: Confidence Intervals (Vocabulary, Quiz, and Practice Exam Questions)

What are degrees of freedom?

1. Degrees of freedom indicate how many values have the freedom to vary 2. Degrees of freedom are often used with critical value tables to interpret a test's results 3. Degrees of freedom are used in calculating the standard deviation of a data set 4. The equation for degrees of freedom is df= N-1

Basin Wind & Sky ski resort signs most of its employees to seasonal, full-time roles. Payroll costs vary from year to year based on dates of operation and snow conditions. Which statistical analysis element allows Basin Wind & Sky to assess these fluctuations as normal rather than abnormal?

Degree of freedom

Which of the following situations would give us the best estimate of a population proportion?

Sample size 150, sample proportion 0.34 (Because among the given option, the largest sample size is 150)

Why is the Z-value statistic useful in calculating a confidence interval?

The Z-value ties the confidence interval to the normal distribution

For a stated confidence interval, what will be the effect of increasing the number of samples?

The confidence interval will apply to a smaller range of data

If we are computing standard deviation, when do we use n-1 degrees of freedom?

When dealing with a sample

Degrees of Freedom

in a statistical calculation represent how many values involved in a calculation have the freedom to vary. Can be calculated to help ensure the statistical validity of chi-square tests, t-tests and even the more advanced f-tests.

Point Estimate

is an unknown statistical value that is essentially a ''best guess'' created for the purpose of projection and analysis when the true value will not be known until a later time

Confidence

is another way to describe probability

Margin of Error

is the number added to or subtracted from the point estimate

Confidence Level

is the percentage of times you expect to reproduce an estimate between the upper and lower bounds of the confidence interval, and is set by the alpha value

Confidence Interval

is the range of values that you expect your estimate to fall between a certain percentage of the time if you run your experiment again or re-sample the population in the same way. It is the mean of your estimate plus and minus the variation in that estimate

Interval Estimation

the range of numbers in which a population parameter lies considering margin of error

T-distribution

which is a kind of symmetric, bell-shaped distribution curve that has a lower height but a wider spread than the standard normal distribution curve

What does a confidence interval of 95% actually mean?

95% of the time the average of the entire population should be in the average range of the sampled data

What do the numbers used to create a confidence interval come from?

A sample of the entire population

What is the tool used in mathematics to make inferences about populations from data?

Estimation An estimation is the tool that is used in mathematics to make inferences about populations from data.

Jia has a sample size of 15. He wants to be able to make inferences about the entire population based on his work. What should he do when calculating his confidence interval?

He should use the t-table to compare calculations because this distribution uses fatter than normal tails under the normal curve to approximate the general population standard deviation. The t-table distribution is an estimation of the general population that allows room for the poor quality of estimation found when using a small sample size deviation as the estimate for the population standard deviation.

All Saints Hospital is using internal research to determine where to open a satellite hospital. The Board of Directors votes to place the new facility in Harristonville because they have concluded that ''hospitals perform better financially when placed in suburban communities.'' This conclusion is an example of a:

Hypothesis

If Mr. Smith polls 240 people and finds that 112 will vote for Bill Jones, which of the following is true?

The sample proportion is .467 To find the sample proportion, divide the number of favorable outcomes in the sample by the total sample size. In this case, 112 yes votes divided by 240 people polled delivers a sample proportion of .467.

A statistician is trying to figure out the sample size needed for an estimation of mu, but they don't know the population standard deviation. What should they do?

They should use a preliminary sample to figure out s and use that instead of sigma