# FREE Bachelor of Science in Industrial Engineering Probability & Statistics Questions and Answers

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#### In a clustering sampling, the chosen clusters are referred to as .

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Clusters are the different groups of people that make up the population. The elementary units in a sample are the chosen clusters.

#### Which of the following situations qualifies as a high sample size?

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A large sample is typically defined as one that contains 30 or more sample values. A sample like this follows a Normal Distribution according to the Central Limit Theorem.

#### Which of the following best represents the population as a whole and is categorized as an exact value?

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A parameter is an accurate or unknowable value that reflects the entire population. Small Roman symbols are typically used to define parameters.

#### If the population is 240 and the sample size is chosen to be 60, the sampling interval is .

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The population is divided into intervals known as sampling intervals. The population/sample size is stated as 240/60, which equals 4.

#### What is the name of a claim made regarding a population for testing purposes?

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A hypothesis is a claim made regarding a population as a whole. Then it is put to the test, accepted if True, and rejected if False. A hypothesis is a claim made regarding a population as a whole. Then it is put to the test, accepted if True, and rejected if False.

#### When the presumption is put to the test and found to be false, what is it called?

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The null hypothesis is one that is considered to be true if the assumed hypothesis is rejected in the test. It provides the population parameter's value.

#### The standard deviation of the sampling distribution is _______ if the sample size is 16 and the population standard deviation is 50.

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The formula for the population standard deviation is provided as /(n)1/2, where n is the sample size and is the population standard deviation. Changing the numbers

σ/(n)1/2
50/(16)1/2
we get ϕ=12.25.

#### What is the underlying presumption behind the T distribution hypothesis test?

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It is assumed that the distribution will follow a normal distribution in order to test the Hypothesis with T distribution. The region is located, and the hypothesis is either accepted or denied based on the normal variate.

#### Determine the value of the f-statistic with a 0.95 cumulative probability.

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The relation with both f – statistic and cumulative probability is given as\sIf f – statistic = f α then, cumulative, probability = (1 – α)  Therefore, f-statistic = (1 - 0.95) = 0.05 for cumulative probability of 0.95

#### What does the parameter k represent in a sampling distribution?

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The parameter k in a sampling distribution denotes the sample interval. It displays the distance between data points.

#### The mean of the sampling distribution must equal _______ if the sample and population distributions vary.

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In a sampling distribution, the population mean is the same as the sampling distribution mean, regardless of sample and population variation. The population mean is the average of all sample means (shown by the x-bars) when repeated random samples of a given size n are selected from a population of values for a quantitative variable where the population mean is and the population standard deviation is (sigma).

#### The process of choosing a suitable subset from a population that encapsulates the traits of the entire population is known as .

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Sampling is the process of picking a suitable subset from a population to represent the traits of the entire population. It helps to combine related samples, making it simpler to manage the distribution.

#### What distribution from the list below is used to compare two variances?

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When comparing two variances is necessary, the F-Distribution is utilized. It compares two variance values using an f-Test.

#### Stratified sampling, systematic sampling, and cluster sampling are examples of .

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Random sampling techniques include systematic samplings, stratified samplings, and cluster samplings. Probability sampling techniques provide the benefit of guaranteeing that the sample picked is representative of the population.

#### What Chi Square distribution resembles a normal distribution the most?

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When the Chi Square distribution has more degrees of freedom, the normal distribution is more likely to be the result. The choice with the most degrees of freedom is one with 16.

#### The mean of the sample distribution is _________ if the population mean is 29.

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If the mean of the population is 29, then the mean of the sampling distribution will also be 29 under typical circumstances. The mean of the sampling distribution tends to be equal to the mean of the population from which the samples are drawn. This is a fundamental concept in statistics known as the "expected value" or "unbiased estimator" property.