Session 4 - Chapter 3 Flashcards
- Calculate standard summary statistics for a given data sample.
- Explain the reasoning inherit in a confidence level.
- Construct a confidence interval.
- Explain the reasoning inherit in a hypothesis test.
- Execute a hypothesis test.
- Outline the roles of deductive and inductive reasoning in making active predictions.
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What are the 2 elements in distribution ?
The population = The universe
(Ex: All the employees of your company)
Random viable
What are the two types of variables ?
1) Random variable
2) Deterministic variable
What are the two types of random variable ?
1) Discrete random variable (Ex: 5, 9, 19, 27, …)
2) Continuous random variable (Ex: Uncountable infinite number of values)
How can you represent the a distribution of random variable ?
You can represent random variable with a probability function.
How can you represent the a distribution of continious random variable ?
You can draw a curve which is the probability density function
What does the graphical for a Normal Random Variable ?
Bell shape
What is the expected value or population mean
E(Xi)
What is the variance
V(X) = E[(Xi - E(Xi))²]
What is the standard deviation of normal random value ?
Standard Deviation = Square root of variable
Sample Size of N
A collection of Nrealizations of Xi ;{Xi,X2…. XN
Voir les slides sur Sample Variance & Sample Standard Deviation
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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
Unbiasedness
A range of values such that there is a specified probability that they contain a population parameter is known as a(n):
confidence interval
An unbiased estimator achieves what sort of property?
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.
If the distribution of one random variable does not depend on the realization of another, the two random variables are considered what?
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.
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?
$5 million
What is the estimator ?
A calculation using sample data that is used to provide information about a population parameter
What is the random sample ?
A sample where every member of the population has an equal chance of being selected
What is an unbiased estimator ?
An estimator whose mean is equal to the population parameter it is used to estimate
What is the Hypothesis test ?
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
What is the Null hypothesis ?
- 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
As the size of the random sample gets larger, what happens to the standard deviation of the distribution for the sample mean?
The distribution for the sample mean gets smaller.
What sample statistic is not likely to be used to construct a confidence interval of a population mean?
You don’t construct a confidence interval with the sample range
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?
There is likely to be skewness in the sample.
In a broad sense, the role of a confidence interval for the population mean is meant to accurately portray what?
The uncertainty involved with observing a sample and not the entire population.
What are the 3 steps of null hypothesis ?
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
For a standard degrees of confidence is 90%, at which p-value do you reject the hypothesis ?
Reject the distribution if the p-value is less than 0.10; fail to reject otherwise. This generates a degree of support of 90%.
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Reject the distribution if the p-value is less than 0.05; fail to reject otherwise. This generates a degree of support of 95%
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Reject the distribution if the p-value is less than 0.01; fail to reject otherwise. This generates a degree of support of 99%
How does Deductive reasoning works ?
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.
How does Inductive reasoning works ?
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
