Best Design of Experiments MCQS with Answers 5

Online Quiz about Design of Experiments MCQs with Answers. There are 20 MCQs in this test. Let us start with “Design of Experiments MCQs with Answer”.

Online Multiple Choice Questions about Design of Experiments with Answers

1. With the passage of time, Statisticians moved from?

 
 
 
 

2. What is the most common one-factor-at-a-time design in social sciences?

 
 
 
 

3. Laboratory experiments are usually performed under:

 
 
 
 

4. Common applications of DOE in management sciences include.

 
 
 
 

5. DOE can be used in management sciences to organize:

 
 
 
 

6. Selection bias (where some groups are underrepresented) is eliminated

 
 
 
 

7. A single performance of an experiment is called?

 
 
 
 

8. The process of choosing experimental units randomly is called

 
 
 
 

9. A phenomenon whose effect on the experimental unit is observed is called.

 
 
 
 

10. Changes in mean scores over three or more time points are compared under the:

 
 
 
 

11. Taguchi designs were presented ———- Plackett-Burman designs.

 
 
 
 

12. Accidental bias (where chance imbalances happen) is minimized through

 
 
 
 

13. Which term is estimated through replication?

 
 
 
 

14. The different states of a factor are called.

 
 
 
 

15. Common applications of DOE in physical sciences include.

 
 
 
 

16. When do experimental factors include the proportions of ingredients we use?

 
 
 
 

17. An important application of DOE in management sciences is to?

 
 
 
 

18. Initial applications of DOE are in?

 
 
 
 

19. An important application of DOE in social sciences is to:

 
 
 
 

20. Physical science is the systematic study of the inorganic world, consisting of astronomy, physics, chemistry, and:

 
 
 
 

Design of Experiments MCQs with Answers

Design of Experiments MCQs with Answers

  • Laboratory experiments are usually performed under:
  • Common applications of DOE in physical sciences include.
  • When do experimental factors include the proportions of ingredients we use?
  • Physical science is the systematic study of the inorganic world, consisting of astronomy, physics, chemistry, and:
  • Common applications of DOE in management sciences include.
  • An important application of DOE in management sciences is to?
  • DOE can be used in management sciences to organize:
  • What is the most common one-factor-at-a-time design in social sciences?
  • An important application of DOE in social sciences is to:
  • Changes in mean scores over three or more time points are compared under the:
  • Initial applications of DOE are in?
  • With the passage of time, Statisticians moved from?
  • Taguchi designs were presented ———- Plackett-Burman designs.
  • Which term is estimated through replication?
  • A single performance of an experiment is called?
  • The different states of a factor are called.
  • A phenomenon whose effect on the experimental unit is observed is called.
  • The process of choosing experimental units randomly is called
  • Accidental bias (where chance imbalances happen) is minimized through
  • Selection bias (where some groups are underrepresented) is eliminated

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One Way Analysis of Variance: Made Easy

The article is about one way Analysis of Variance. In the analysis of variance, the total variation in the data of the sample is split up into meaningful components that measure different sources of variation. Each component yields an estimate of the population variance, and these estimates are tested for homogeneity by using the F-distribution.

One Way Classification (Single Factor Experiments)

The classification of observations based on a single criterion or factor is called a one-way classification.

In single factor experiments, independent samples are selected from $k$ populations, each with $n$ observations. For samples, the word treatment is used and each treatment has $n$ repetitions or replications. By treatment, we mean the fertilizers applied to the fields, the varieties of a crop sown, or the temperature and humidity to which an item is subjected in a production process. The collected data consisting of $kn$ observations ($k$ samples of $n$ observations each) can be presented as.

One way analysis of variance

where

$X_{ij}$ is the $i$th observation receiving the $j$th treatment

$X_{\cdot j}=\sum\limits_{i=1}^n X_{ij}$ is the total observations receiving the $j$th treatment

$\overline{X}_{\cdot j}=\frac{X_{\cdot j}}{n}$ is the mean of the observations receiving the $j$th treatment

$X_{\cdot \cdot}=\sum\limits_{i=j}^n X_{\cdot j} = \sum\limits_{j=1}^k \sum\limits_{i=1}^n X_{ij}$ is the total of all observations

$\overline{\overline{X}} = \frac{X_{\cdot \cdot}}{kn}$ is the mean of all observations.

The $k$ treatments are assumed to be homogeneous, and the random samples taken from the same parent population are approximately normal with mean $\mu$ and variance $\sigma^2$.

Design of Experiments

One Way Analysis of Variance Model

The linear model on which the one way analysis of variance is based is

$$X_{ij} = \mu + \alpha_j + e_{ij}, \quad\quad i=1,2,\cdots, n; \quad j=1,2,\cdots, k$$

Where $X_{ij}$ is the $i$th observation in the $j$th treatment, $\mu$ is the overall mean for all treatments, $\alpha_j$ is the effect of the $j$th treatment, and $e_{ij}$ is the random error associated with the $i$th observation in the $j$th treatment.

The One Way Analysis of Variance model is based on the following assumptions:

  • The model assumes that each observation $X_{ij}$ is the sum of three linear components
    • The true mean effect $\mu$
    • The true effect of the $j$th treatment $\alpha_j$
    • The random error associated with the $j$th observation $e_{ij}$
  • The observations to which the $k$ treatments are applied are homogeneous.
  • Each of the $k$ samples is selected randomly and independently from a normal population with mean $\mu$ and variance $\sigma^2_e$.
  • The random error $e_{ij}$ is a normally distributed random variable with $E(e_{ij})=0$ and $Var(e_{ij})=\sigma^2_{ij}$.
  • The sum of all $k$ treatments effects must be zero $(\sum\limits_{j=1}^k \alpha_j =0)$.

Suppose you are comparing crop yields that were fertilized with different mixtures. The yield (numerical) is the dependent variable, and fertilizer type (categorical with 3 levels) is the independent variable. ANOVA helps you determine if the fertilizer mixtures have a statistically significant effect on the average yield.

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Important Testing of Hypothesis MCQs 8

The quiz is about Testing of Hypothesis MCQs with Answers. The quiz contains 20 questions about hypothesis testing. It covers the topics of formulation of the null and alternative hypotheses, level of significance, test statistics, region of rejection, and decision about acceptance and rejection of the hypothesis. Let us start with the Testing of Hypothesis MCQs quiz.

Please go to Important Testing of Hypothesis MCQs 8 to view the test

Testing of Hypothesis MCQs with Answers

Hypothesis Testing procedure
  • In hypothesis testing, the hypothesis which is tentatively assumed to be true is called the
  • When the null hypothesis has been true, but the sample information has resulted in the rejection of the null, a ———- has been made.
  • The maximum probability of a Type I error that the decision-maker will tolerate is called the
  • A Type II error is the error of
  • In hypothesis testing, the level of significance is
  • For finding the p-value when the population standard deviation is unknown, if it is reasonable to assume that the population is normal, we use
  • In hypothesis testing, $\beta$ is
  • A hypothesis test in which rejection of the null hypothesis occurs for values of the point estimator in either tail of the sampling distribution is called
  • When testing the following hypotheses at a level of significance $H_o: p \le 0.7$ $H_a: p > 0.7$ The null hypothesis will be rejected if the test statistic $Z$ is
  • Which of the following does not need to be known to compute the P-value?
  • Which of the following statements is false?
  • If you reject a true null hypothesis, what does this mean?
  • How do you commit a Type II error?
  • What test should a researcher use to determine whether there is evidence that the mean family income in the U.S. is greater than $30,000?
  • In a hypothesis test, the probability of obtaining a value of the test statistic equal to or even more extreme than the value observed, given that the null hypothesis is true, is referred to as what?
  • If the p-value is greater than alpha in a two-tail test, what conclusion should you draw?
  • If the p-value is less than alpha in a one-tail test, what conclusion can you draw?
  • If a one-tail Z test for a proportion is performed and the upper critical value is +2.33 and the test statistic is equal to +1.37, then what conclusion can you draw?
  • What is the region of rejection for a one-tail Z test?
  • What determines how close the computed sample statistic has come to the hypothesized population parameter?
Testing of Hypothesis MCQs Quiz

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Index Number in Statistics: made easy

An index number in statistics is a tool used to track changes in a variable or a group of related variables, typically over time. Index Numbers condense the complex data into a single number (expressed as a percentage) for easier comparison between different periods or situations.

Example: A factory manager may wish to compare this month’s per-unit production cost with that of the past 6 months.

An index number measures how much a variable changes over time.

Simple Relatives Index Numbers

A simple relative is a ratio of the value of a variable in a given period to its value in the base (or reference) period.

If $x_0$ and $x_n$ are the values of a variable during the base period and a given period, respectively, then the simple relative, denoted by $x_{0n}$ is
$$x_{0n}=\frac{x_n}{x_0}$$

A relative is usually expressed as a percentage by multiplying by 100.

Simple Price Relative

If $p_0$ and $p_n$ are the prices of a commodity \texturdu{مفید شے، مال اسباب} during the base period and a given period, respectively, then the simple price relative, denoted by $p_{0n}$ is
$$p_{0n}=\frac{p_n}{p_0}$$
The price is generally defined as “money per unit quantity” and is usually taken as the average price for a period because the prices are not constant throughout a period.

Simple Quantity (Volume) Relative

If $q_0$ and $q_n$ are quantities of a commodity (produced, consumed, purchased, sold, exported, or imported, etc.) during the base period and a given period, respectively, then the simple quantity relative, denoted by $q_{0n}$ is
$$q_{0n}=\frac{q_n}{q_0}$$

Value

If $p$ is the price of a commodity and $q$ is its quantity during a period, then the value $v$ is given by $v=p\,q$. For example, if a quantity of 560kg of a commodity is purchased at the rate of Rs. 5 per Kg then
$$v=pq=5\times 560 = 2800$$

Simple Value Relative

If $v_0$ and $v_n$ are the values of a commodity during the base period and a given period, respectively, then the simple value relative, denoted by $v_{0n}$ is
$$v_{0n}=\frac{v_n}{v_0}=\frac{p_nq_n}{p_0q_0}=\frac{p_n}{q_n}\times \frac{q_n}{q_0}=p_{0n}\times q_{0n}$$

Index Number in Statistics

Uses of Index Number in Statistics

  • Functions: Measure changes in variables like prices, production levels, or stock values.
  • Benefits:
    • Simplifies complex data comparisons
    • Tracks trends over time
    • Provides a benchmark for analysis (often using a base period as a reference point at 100)
  • Examples:
    • Consumer Price Index (CPI) tracks inflation by measuring changes in the prices of a basket of goods and services.
    • Stock market indices like the S&P 500 track the overall performance of a specific stock market section.

Note that there are various types of index numbers used for different purposes. Computing the index numbers involves specific formulas and functions that take into account the chosen base period and the way different variables are weighted within the index.

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