Explanation

When testing a null hypothesis, there are two types of errors that can occur:

• Type I error (α-error): Rejecting the null hypothesis when it is actually true (false positive).
• Type II error (β-error): Failing to reject the null hypothesis when it is actually false (false negative).

Explanation

Design of experiments (DOE) is commonly used to:

• Develop new processes
• Improve existing processes
• Optimize process parameters
• Reduce variability
• Improve product quality

Explanation

• A sample statistic is a numerical value that summarizes a characteristic of a sample.
• Such as the sample mean, sample proportion, sample variance, etc.

Explanation

• Control charts and procedures of descriptive statistics used to enhance a process are classified as Statistical Process Control (SPC) tools.
• SPC is a methodology that uses statistical techniques to monitor and control processes to ensure they operate within predetermined limits.

Explanation

• When the number of unknowns is greater than the number of equations, the system is underdetermined, and there is no unique solution.
• In such cases, we use the method of least squares to estimate the unknowns.

Explanation

• Multiple regression is a statistical technique that examines the relationship between a dependent variable (outcome variable) and two or more independent variables (predictor variables).
• It helps to predict the value of the dependent variable based on the values of the independent variables.

Explanation

• The phrase "to read between the lines" is an idiomatic expression that means to infer or understand the implicit or hidden meaning of a text, situation, or conversation, beyond the literal or obvious interpretation.
• It requires a deeper understanding and interpretation of the context.

Explanation

• Simple correlation, also known as Pearson's r.
• It is a statistical technique used to measure the strength and direction of the linear relationship between two continuous variables, X and Y.
• It is called "simple" because it involves only two variables.

Explanation

The Poisson distribution is a discrete probability distribution that models the number of events (k) occurring in a fixed interval of time or space.

The probability mass function of the Poisson distribution is:

P(k) = (e^(-m) * (m^k)) / k!

where m is the mean (expected value) of the distribution, and e is the base of the natural logarithm (approximately 2.718).

If the mean (m) of a Poisson distribution is 1, then the probability of P(1) is:

P(1) = (e^(-1) * (1^1)) / 1! = 1/e ≈ 0.3679

So, the probability of P(1) is approximately 0.368, or 1/e.

Explanation

• A sample statistic is a measure calculated from a smaller group of individuals (a sample) taken from a larger population.
• While a population parameter is a measure of the entire population.