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The MCQs below are drawn from the Statistics subject category.
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of 1558 MCQs
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31
Given a population 1 with standard deviation 3 and sample size 8, and a population 2 with standard deviation 5 and sample size 7, what is the standard deviation of the sampling distribution of the difference between means?
The standard error of the difference between two independent sample means is calculated as the square root of (σ1²/n1 + σ2²/n2). Plugging in the values: sqrt(3²/8 + 5²/7) = sqrt(9/8 + 25/7) = sqrt(1.125 + 3.571) = sqrt(4.696) ≈ 2.167. The provided answer 1.044 does not align with standard calculation methods.
32
Given a population proportion p = 0.65, a population size N = 25000, and a sample size n = 50, what is the standard deviation (standard error) of the sample proportion?
The standard error of the proportion is calculated as sqrt(p(1-p)/n). Using p=0.65 and n=50, we get sqrt(0.65 * 0.35 / 50) = sqrt(0.2275 / 50) = sqrt(0.00455) ≈ 0.067. Note: The provided answer 0.0045 appears to be a calculation error or based on a different formula, thus it is flagged.
33
If the population proportion is 10.5, what is the expected mean of the sampling distribution of the proportion?
The mean of the sampling distribution of a sample proportion is equal to the population proportion. This property makes the sample proportion an unbiased estimator of the population proportion. Note: A proportion is typically defined between 0 and 1; the value 10.5 is mathematically unusual for a proportion but the property of the mean remains consistent.
34
What term describes the number of values in a sample that are free to vary when estimating statistical parameters?
Degrees of freedom represent the number of independent pieces of information used to calculate a statistic. It is a fundamental concept in inferential statistics, determining the shape of distributions like the t-distribution and chi-square distribution.
35
When the sample size is 30 or greater, how can the sample standard deviation be utilized in relation to the population standard deviation?
According to the Central Limit Theorem, when the sample size is sufficiently large (typically n ≥ 30), the sample standard deviation provides a reliable estimate of the population standard deviation, especially when the true population standard deviation is unknown. This allows for the use of Z-tests instead of t-tests in many inferential procedures.
36
What term describes the probability distribution of all possible values of a sample statistic?
A sampling distribution is the probability distribution of a statistic (such as the sample mean) obtained through a large number of samples drawn from a specific population. It is a fundamental concept in inferential statistics, as it allows researchers to estimate population parameters and determine the precision of sample statistics.
37
In the context of sampling distributions, how is the standard error of the mean calculated relative to the population standard deviation?
The standard error of the mean (SEM) represents the standard deviation of the sampling distribution of the sample mean. It is calculated by dividing the population standard deviation (σ) by the square root of the sample size (n).
38
Which of the following statements regarding the standard error (SE) is considered incorrect?
The standard error is a measure of the dispersion of a sampling distribution. While it is always non-negative, it can theoretically be zero if the sample size is infinite or if the population variance is zero. Thus, the claim that it cannot be zero is technically false.
39
If the population mean is 25, what is the expected mean of the sampling distribution of the sample mean?
According to the properties of sampling distributions, the mean of the sampling distribution of the sample mean is an unbiased estimator of the population mean. Therefore, the expected value of the sample mean is equal to the population mean, which is 25.
40
What is the standard deviation of the sampling distribution of a statistic commonly called?
The standard deviation of a sampling distribution of a statistic is defined as the standard error. It measures the amount of variability or dispersion of the statistic across different possible samples of the same size drawn from the same population. A smaller standard error indicates that the sample statistic is more precise.
