Confidence Intervals

Question 1

What is the definition of Confidence Intervals?

Answer 1

The range within which you expect the population parameter to be.

It’s estimation is based on the data we have in our sample

A confidence interval is a much more accurate representation of reality

Question 2

Can you be 100% confident?

Answer 2

no - unless you go through the entire population

Question 3

What is the Level of Confidence denoted as?

Answer 3

1-alpha (one minus alpha)
it is called the confidence level of the interavl

Question 4

What is the value range of Alpha

Answer 4

0-1

Question 5

How is a confidence interval related to a point estimate?

Answer 5

The point estimate is the midpoint of the interval.

Question 6

What are the two main situations when calculating Confidence Intervals?

Answer 6

When the Population Variance is Known and when it is Unknown

Question 7

What is the Reliability Factor?

Answer 7

Z alpha / 2

Question 8

What are different Alpha levels?

Answer 8

Confidence level = 95%
alpha = 5%

Confidence level = 99%
alpha = 1%

Question 9

What are common Confidence Levels?

Answer 9

90%, 95%, 99%
a = 10%, 5%, 1%
a = 0.1, 0.05, 0.01

Question 10

What does a 95% Confidence Level mean?

Answer 10

A 95% confidence interval means that you are sure that in 95% of the cases, the true population parameter would fall into the specified interval

Question 11

Where does the z of alpha come from?

Answer 11

The z-table. The Standard Normal Distribution table

Question 12

What is a commonly used term for the Z?

Answer 12

critical value

Question 13

A more narrow confidence interval translates into?

Answer 13

higher uncertainty

Question 14

There is a tradeoff between the level of confidence and what?

Answer 14

The range of the interval

Question 15

What is the accepted norm for Confidence Levels?

Answer 15

95%

Question 16

What is the formula for Standard Error

Answer 16

SE = sample standard deviation / sqrt(n)

Question 17

What is significant about Student’s T?

Answer 17

It allows you to make inferences through small samples with unknown population variance and applies to a large number of real life situations

Question 18

What do fatter tails allow for?

Answer 18

Allows for a higher dispersion of variables and there is more uncertainty

Question 19

What is the formula for calculating the z-statistic Confidence Interval?

Answer 19

mean +- z-stat * std error

Question 20

The z-statistic is related to what distribution?

Answer 20

The standard normal distribution

Question 21

The t-statistic is related to what distribution?

Answer 21

Student’s T distribution

Question 22

What is a degree of freedom in Student T distributions calculated?

Answer 22

degrees of freedom are equal to n-1

Question 23

At what number of samples should you use the z table instead of the t table?

Answer 23

50

Question 24

What is the formula to calculate a t-score with unknown variance Confidence Interval?

Answer 24

x-bar (mean) +- tn-1, a/2 * stderror
or
mean +- t-stat * std error

Question 25

What is the Excel formula for calculating the t-stat

Answer 25

=T.INV.2T(CI ie 0.05, DF)

Question 26

What is the Excel formula for calculating the z-stat?

Answer 26

=NORMSINV(0.95 probability) probability = 1-(alpha/2)

90% =NORMSINV(0.95) = 1.64
95% =NORMSINV(0.975) = 1.96
99% =NORMSINV(0.995) = 2.58

Question 27

What do we get when we know the Population Variance?

Answer 27

we get a narrower confidence interval

Question 28

What do we get when we do not know the Population Variance?

Answer 28

We get a wider confidence interval - a higher level of uncertainty

Question 29

What is proper statistic for estimating the confidence interval when the population variance in unknown?

Answer 29

The t-statistic

Question 30

The formula’s z & t determine the span of the confidence interval. What is their special name?

Answer 30

Margin of Error

Question 31

Getting a smaller margin of error would mean what in relation to the confidence interval?

Answer 31

it would get narrower

Question 32

What is the difference between dependent and independent samples?

Answer 32

it’s important to know whether your samples are dependent or independent: If the values in one sample affect the values in the other sample, then the samples are dependent. If the values in one sample reveal no information about those of the other sample, then the samples are independent.

Question 33

What is an example use of dependent samples?

Answer 33

When researching the same sample over time - looking at the same person before and after

When developing medicine

When looking at families - habits of husbands and wives.

Cause and effect

Question 34

With independent Samples, what 3 cases can we further distinguish?

Answer 34

1. When the population variance is known
2. When the population variance is unknown but assumed to be equal
3. When the population variance is unknown but assumed to be different

Question 35

What is the Excel formula for calculating confidence intervals for t-stat?

Answer 35

=CONFIDENCE.T()

=CONFIDENCE.T(0.1,$H$16, 10) - 90%
=CONFIDENCE.T(0.05,$H$16, 10) - 95%
=CONFIDENCE.T(0.01,$H$16, 10) - 99%

Question 36

An increase in the confidence level will result in______.

Answer 36

a wider confidence interval

Question 37

“Suppose that you want to know the average height of people living in a town with 2,000 residents. You take a sample of 50 inhabitants, measure them, and find that the mean height is 5 feet 9 inches (5’94). In this case, the sample mean is the parameter, the population mean is the estimator, and 5’9” is the estimate.”

Answer 37

Patrick is wrong - the sample mean is the estimator, the population mean is the parameter, and the result of 5’9” is the estimate

Explanation of correct answer:
The parameter is a particular attribute of population, whereas the sample mean is a statistic that estimates some fact about the population. In this case, the sample mean is an estimator of the population mean. The estimate, on the other hand, is a specific value produced by the estimator.