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Answer: To analyze the given information about a sample population, first, let's look at what we have: a sample size (n) of 400 individuals and a sample proportion (p̂) of 0.175. The sample proportion represents the fraction of the sample that has a particular characteristic. In this case, 0.175 of the sample exhibits this characteristic.
Now, let's break down the numbers: - The sample size: n = 400 - The sample proportion (also known as the observed proportion): p̂ = 0.175
From the sample proportion, we can calculate the number of individuals in the sample who exhibit the characteristic by multiplying the sample size by the sample proportion: Number with characteristic = n * p̂ = 400 * 0.175 = 70
So, in a sample of 400 individuals, 70 of them have the characteristic corresponding to the sample proportion of 0.175.
If desired, you can use this information to calculate other statistics such as the standard error of the proportion, confidence intervals, or to conduct hypothesis tests, if you are working within the context of a statistical analysis.
Extra: The sample proportion is an important statistic in inferential statistics, which is the branch of statistics that allows us to make generalizations from a sample to a larger population. It is often denoted by p̂, and it is a point estimate of the true population proportion (p). We assume that the sample is representative of the population from which it was drawn, which allows us to estimate the percentage of the population that exhibits the characteristic based on the sample.
A key aspect of understanding sample proportions is understanding the Law of Large Numbers, which suggests that as the sample size increases, the sample proportion will generally get closer to the true population proportion.
Hypothesis testing might be used with a sample proportion to determine if there is enough evidence to support a specific claim about the population proportion. Confidence intervals can also be constructed around the sample proportion to give a range of plausible values for the true population proportion with a certain level of confidence (e.g., 95% confidence interval).
However, it is also important to consider sampling methods and potential biases. A simple random sample is usually required to ensure that the results are representative of the population. If the sample is biased or not randomly selected, the estimations made from the sample proportion may not reliably represent the population.