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Answer :
Q1 If you averaged every person in the population, the result would be Mu, but the mean of a sample, or xbar, would be the average value discovered in the sample.
Q2 For the group being tested, each point in a sample distribution represents a potential outcome variable.
Q3 The random condition is very important because it simplifies the sample and prevent possible bias in the sampling.
Q4 To make sure that the observations in the sample are nearly independent, it is crucial to evaluate the 10% condition before calculating probability involving x.
Q5 The big counts criterion ensures that there are more successes than failures for a normally distributed set of results. The need for big numbers is np ≥10 and n(1-p) ≥10.
Q6 For a variety of reasons, finding unbiased estimates for those seeking asylum may be challenging. First, because of persecution, these people are escaping their country.
Q7 there is less spread for larger sample than that of lower sample.
What is meant by sampling distribution?
The probability distribution of a statistic acquired from a bigger sample size taken from a certain population is known as the sampling distribution.
What is the purpose of sampling distribution?
Based on the data they have available, sampling distributions are useful tools used by researchers to estimate and draw conclusions about a wider population of interest.
Q1 If you averaged every person in the population, the result would be Mu, but the mean of a sample, or xbar, would be the average value discovered in the sample.
Q2 For the group being tested, each point in a sample distribution represents a potential outcome variable.
Q3 The random condition is very important because it simplifies the sample and prevent possible bias in the sampling.
Q4 To make sure that the observations in the sample are nearly independent, it is crucial to evaluate the 10% condition before calculating probability involving x.
Q5 The big counts criterion ensures that there are more successes than failures for a normally distributed set of results. The need for big numbers is np ≥10 and n(1-p) ≥10.
Q6 For a variety of reasons, finding unbiased estimates for those seeking asylum may be challenging. First, because of persecution, these people are escaping their country.
Q7 there is less spread for larger sample than that of lower sample.
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Final answer:
Mu (μ) is the population mean while x bar is the sample mean. Checking various conditions like the random, 10%, and large counts conditions helps ensure the reliability of statistical methods. The size of a sample influences the spread in the sampling distribution: larger samples result in a smaller spread.
Explanation:
Differences between "mu" and "x bar"
The difference between "mu" (μ) and "x bar" is that μ represents the population mean, which is the average value of a particular variable across the entire population. In contrast x-bar represents the sample mean, which is the average value of that variable across a sample drawn from the population.
Sampling Distribution:
Each "point" in a sampling distribution for a mean represents the mean of an individual sample taken from the population
Checking Conditions:
The purpose of checking the random condition is to ensure that each sample is drawn randomly and independently from the population. This helps to ensure that the sample is representative of the population. The 10% condition is checked to ensure that the sample size is less than 10% of the population, which makes the samples more independent. The large counts condition involves ensuring that the expected number of successes and failures is large enough, typically at least 5, to use normal approximation for the binomial distribution.
Challenges in Unbiased Estimations:
It is difficult to find unbiased estimates about asylum-seekers due to various factors like sample bias, unavailability of comprehensive data, and political or social barriers to conducting thorough research.
Influence of Sample Size on Spread:
Dividing the standard deviation by the square root of the sample size (n) to calculate the standard error of the sampling distribution for a proportion influences the spread. When sample sizes are high, the spread is smaller, indicating more precision. When sample sizes are low, the spread is larger, indicating less precision.
