Session 4 - Chapter 3

Question 1

1. Calculate standard summary statistics for a given data sample.
2. Explain the reasoning inherit in a confidence level.
3. Construct a confidence interval.
4. Explain the reasoning inherit in a hypothesis test.
5. Execute a hypothesis test.
6. Outline the roles of deductive and inductive reasoning in making active predictions.

Answer 1

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Question 2

What are the 2 elements in distribution ?

Answer 2

The population = The universe
(Ex: All the employees of your company)

Random viable

Question 3

What are the two types of variables ?

Answer 3

1) Random variable

2) Deterministic variable

Question 4

What are the two types of random variable ?

Answer 4

1) Discrete random variable (Ex: 5, 9, 19, 27, …)

2) Continuous random variable (Ex: Uncountable infinite number of values)

Question 5

How can you represent the a distribution of random variable ?

Answer 5

You can represent random variable with a probability function.

Question 6

How can you represent the a distribution of continious random variable ?

Answer 6

You can draw a curve which is the probability density function

Question 7

What does the graphical for a Normal Random Variable ?

Answer 7

Bell shape

Question 8

What is the expected value or population mean

Answer 8

E(Xi)

Question 9

What is the variance

Answer 9

V(X) = E[(Xi - E(Xi))²]

Question 10

What is the standard deviation of normal random value ?

Answer 10

Standard Deviation = Square root of variable

Question 11

Sample Size of N

Answer 11

A collection of Nrealizations of Xi ;{Xi,X2…. XN

Question 12

Voir les slides sur Sample Variance & Sample Standard Deviation

Answer 12

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Question 13

When calculating the sample variance of a random sample, you divide the sum of the squared deviations (from the sample mean) by N - 1 instead of N to ensure the estimator achieves what property

Answer 13

Unbiasedness

Question 14

A range of values such that there is a specified probability that they contain a population parameter is known as a(n):

Answer 14

confidence interval

Question 15

An unbiased estimator achieves what sort of property?

Answer 15

Its mean is equal to the population parameter it is used to estimate.
Explanation: An unbiased estimator is an estimator whose mean is equal to the population parameter it is used to estimate.

Question 16

If the distribution of one random variable does not depend on the realization of another, the two random variables are considered what?

Answer 16

Independent

Explanation: The assumption of a random sample implies that each variable is independent, which means that the distribution of one random variable does not depend on the realization of another.

Question 17

Suppose a sample of five retail stores’ monthly profits are: $4,000, $7,000, $5,000, $3,000, and $1,000. What will the sample variance of stores profits be?

Answer 17

$5 million

Question 18

What is the estimator ?

Answer 18

A calculation using sample data that is used to provide information about a population parameter

Question 19

What is the random sample ?

Answer 19

A sample where every member of the population has an equal chance of being selected

Question 20

What is an unbiased estimator ?

Answer 20

An estimator whose mean is equal to the population parameter it is used to estimate

Question 21

What is the Hypothesis test ?

Answer 21

Hypothesis test is the process of using sample data to assess the credibility of a hypothesis about a population
Making an assessment
• Reject the hypothesis
• Fail to reject the hypothesis

Question 22

What is the Null hypothesis ?

Answer 22

• The hypothesis to be tested using a data sample
• Written as H0: μ= K, where K is the hypothesized value for the population mean
• The objective is to determine whether the null hypothesis is credible given the data we observe.
• If a sample of size Nis a random sample

Question 23

As the size of the random sample gets larger, what happens to the standard deviation of the distribution for the sample mean?

Answer 23

The distribution for the sample mean gets smaller.

Question 24

What sample statistic is not likely to be used to construct a confidence interval of a population mean?

Answer 24

You don’t construct a confidence interval with the sample range

Question 25

Suppose you send out 350 surveys to random sample of all past customers (your target population) asking them to report their level of satisfaction with your product. Of the 350, you used the 112 that responded to the survey to construct a confidence interval for the population “satisfaction score.” What might be a potential problem with this confidence interval?

Answer 25

There is likely to be skewness in the sample.

Question 26

In a broad sense, the role of a confidence interval for the population mean is meant to accurately portray what?

Answer 26

The uncertainty involved with observing a sample and not the entire population.

Question 27

What are the 3 steps of null hypothesis ?

Answer 27

3 Steps in Hypothesis Testing:

1) State the null hypothesis
2) Collect the data sample and calculate the sample mean
3) Decide whether or not to reject the deduced distribution for the sample mean
3) a) Degree of support
3) b) Measure how many standard deviations the sample mean is from the hypothesized population mean

Question 28

For a standard degrees of confidence is 90%, at which p-value do you reject the hypothesis ?

Answer 28

Reject the distribution if the p-value is less than 0.10; fail to reject otherwise. This generates a degree of support of 90%.

Question 29

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Answer 29

Reject the distribution if the p-value is less than 0.05; fail to reject otherwise. This generates a degree of support of 95%

Question 30

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Answer 30

Reject the distribution if the p-value is less than 0.01; fail to reject otherwise. This generates a degree of support of 99%

Question 31

How does Deductive reasoning works ?

Answer 31

Deductive reasoning: Make assumptions that imply causality between X and Y and the distribution of an estimator for the magnitude of this causality in the population.

Question 32

How does Inductive reasoning works ?

Answer 32

Inductive reasoning: Using an observed data sample, build a confidence interval and/or determine whether to reject a null hypothesis for the magnitude of the population-level causalit