Important MCQs Sampling Distribution Quiz with Answer 11

Online Sampling Distribution Quiz with Answers for the preparation of exams and different statistical job tests in Government/ Semi-Government or Private Organization sectors. This Online Quiz about Sampling Distributions is also helpful in getting admission to various colleges and Universities. There are 20 Multiple Choice Type Questions from the Sampling and Sampling Distribution Quiz. Let us start with the Sampling Distribution Quiz.

Online Multiple Choice Questions about Sampling and Sampling Distributions with Answers

1. Regardless of the difference in the distribution of the sample and population, the mean of sampling distribution must be equal to

 
 
 
 

2. A group consists of 300 people and we are interviewing all members of a given group called:

 
 
 
 

3. Consider a population of size 700 consisting of three strata such that $N_1=100, N_2=250$, and $N_3=350$. The required sample size is 18. What will be the sample size for stratum-II according to proportional allocation?

 
 
 
 

4. The university has 5000 students belonging to the following classes: (i) 1500 are freshmen, (ii) 1200 are sophomores, (iii) 1400 are juniors, and (iv) 900 are seniors. The university administration wants to get an estimate of all the student’s views on a proposal to help alleviate the parking problem on campus. Suppose, that a sample of 100 students is chosen, what is the required sample size for the freshman stratum under proportional allocation?

 
 
 
 

5. The margin of error is the level of _________ you require.

 
 
 

6. Which one of the following is the benefit of using simple random sampling?

 
 
 
 

7. Sampling in which a sampling unit can be repeated more than once is called

 
 
 
 

8. Consider a population of size 700 consisting of three strata such that $N_1=100, N_2=250$, and $N_3=350$. The required sample size is 18. What will be the sample size for stratum-III according to proportional allocation?

 
 
 
 

9. A procedure in which the number of elements in a stratum is proportional to the number of elements in the population is called

 
 
 
 

10. The weight of the stratum is equal to the proportion of:

 
 
 
 

11. Which one of these sampling methods is a probability method?

 
 
 
 

12. When the number of observations drawn from a stratum is small relative to the overall size of the stratum then the ————- will also be small.

 
 
 
 

13. Which one of the following is the main problem with using non-probability sampling techniques?

 
 
 
 

14. The value of $n_2$ by a proportional allocation from the following information is:
$N_1=580$, $N_2=140$ and $n=80$.

 
 
 
 

15. When the sample size increases, everything else remains the same, and the width of a confidence interval for a population parameter will

 
 
 
 

16. When sampling is done with or without replacement, $E(\overline{y})$ is equal to

 
 
 
 

17. When the procedure of selecting the elements from the population is not based on probability is known as:

 
 
 
 

18. The weight of the stratum is equal to the proportion of

 
 
 
 

19. Stratification is to produce estimators with small

 
 
 

20. If a researcher randomly samples 100 observations in each population category then his ————— sample will be ———-.

 
 
 
 


MCQs Sampling Distribution Quiz with Answers

  • The weight of the stratum is equal to the proportion of:
  • A group consists of 300 people and we are interviewing all members of a given group called:
  • When the procedure of selecting the elements from the population is not based on probability is known as:
  • The university has 5000 students belonging to the following classes: (i) 1500 are freshmen, (ii) 1200 are sophomores, (iii) 1400 are juniors, and (iv) 900 are seniors. The university administration wants to get an estimate of all the student’s views on a proposal to help alleviate the parking problem on campus. Suppose, that a sample of 100 students is chosen, what is the required sample size for the freshman stratum under proportional allocation?
  • When the sample size increases, everything else remains the same, and the width of a confidence interval for a population parameter will
  • The value of $n_2$ by a proportional allocation from the following information is: $N_1=580$, $N_2=140$ and $n=80$.
  • Sampling in which a sampling unit can be repeated more than once is called
  • Which one of these sampling methods is a probability method?
  • Which one of the following is the main problem with using non-probability sampling techniques?
  • Which one of the following is the benefit of using simple random sampling?
  • When sampling is done with or without replacement, $E(\overline{y})$ is equal to
  • The margin of error is the level of ———- you require.
  • If a researcher randomly samples 100 observations in each population category then his ————— sample will be ———-.
  • Stratification is to produce estimators with small
  • The weight of the stratum is equal to the proportion of
  • When the number of observations drawn from a stratum is small relative to the overall size of the stratum then the ————- will also be small.
  • Regardless of the difference in the distribution of the sample and population, the mean of sampling distribution must be equal to
  • A procedure in which the number of elements in a stratum is proportional to the number of elements in the population is called
  • Consider a population of size 700 consisting of three strata such that $N_1=100, N_2=250$, and $N_3=350$. The required sample size is 18. What will be the sample size for stratum-II according to proportional allocation?
  • Consider a population of size 700 consisting of three strata such that $N_1=100, N_2=250$, and $N_3=350$. The required sample size is 18. What will be the sample size for stratum-III according to proportional allocation?
MCQs Sampling and Sampling Distribution Quiz with Answers

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A sampling distribution depends on several factors:

  • The statistic being used: Is the researcher looking at the mean, median, or something else?
  • The original population’s distribution: Is the population data normally distributed, skewed, or something else?
  • Sample size: Generally, larger samples lead to sampling distributions closer to the actual population distribution.
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In conclusion, sampling distributions are vital tools in statistics. Sampling Distributions help us to understand the variability of statistics calculated from samples and make informed inferences about the population from which the samples were drawn.

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”.

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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.

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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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