one-sample test

简明释义

单样本检验

英英释义

例句

1.Using a one-sample test, we were able to confirm that the average daily sales exceeded our target.

通过使用单样本检验，我们证实了平均每日销售额超过了我们的目标。

2.Before launching the new product, we performed a one-sample test to see if customer satisfaction ratings met our standards.

在推出新产品之前，我们进行了一个单样本检验以查看客户满意度评分是否符合我们的标准。

3.The results of the one-sample test showed that the mean score of the class was significantly higher than the expected value.

这个单样本检验的结果显示，该班的平均分数显著高于预期值。

4.In our research, we conducted a one-sample test to determine if the average height of students in our school differs from the national average.

在我们的研究中，我们进行了一个单样本检验以确定我们学校学生的平均身高是否与全国平均水平不同。

5.In psychology, researchers often use a one-sample test to compare sample means against a known population mean.

在心理学中，研究人员经常使用单样本检验将样本均值与已知的总体均值进行比较。

作文

In the field of statistics, conducting a hypothesis test is essential for making inferences about a population based on sample data. One common type of hypothesis test is the one-sample test, which is used when we want to determine whether the mean of a single sample differs significantly from a known or hypothesized population mean. This method is particularly useful in various fields such as psychology, medicine, and quality control, where researchers often need to assess whether their sample data provides enough evidence to support a specific claim about a population. To perform a one-sample test, one must first formulate a null hypothesis (H0) and an alternative hypothesis (H1). The null hypothesis typically states that there is no significant difference between the sample mean and the population mean, while the alternative hypothesis suggests that a difference does exist. For example, if a researcher wants to test whether the average height of a group of students differs from the national average of 170 cm, they would set up their hypotheses accordingly. Next, the researcher collects data from the sample and calculates the sample mean and standard deviation. Using this information, they can compute a test statistic, which will help determine how far the sample mean is from the population mean in terms of standard deviations. Commonly used test statistics for a one-sample test include the t-statistic and z-statistic, depending on the sample size and whether the population standard deviation is known. Once the test statistic is calculated, the researcher compares it to a critical value from the appropriate statistical distribution to decide whether to reject or fail to reject the null hypothesis. If the test statistic falls within the critical region, the null hypothesis is rejected, indicating that there is a statistically significant difference between the sample mean and the population mean. Conversely, if the test statistic does not fall within the critical region, the null hypothesis remains accepted, suggesting no significant difference exists. Moreover, it is crucial to consider the significance level (alpha) when performing a one-sample test. The significance level represents the probability of rejecting the null hypothesis when it is actually true. A common choice for alpha is 0.05, meaning there is a 5% risk of concluding that a difference exists when there is none. Understanding the implications of this level is vital for researchers to avoid making erroneous conclusions based on their data. In conclusion, the one-sample test is a powerful statistical tool that enables researchers to make informed decisions about population parameters based on sample data. By carefully formulating hypotheses, calculating test statistics, and interpreting results, researchers can draw meaningful conclusions that contribute to their respective fields. Whether in academic research, medical studies, or industrial applications, mastering the one-sample test is essential for anyone looking to leverage statistics for informed decision-making.

在统计学领域，进行假设检验对于根据样本数据对总体进行推断至关重要。一种常见的假设检验类型是单样本检验，当我们想要确定单个样本的均值是否显著不同于已知或假设的总体均值时，就会使用这种方法。这种方法在心理学、医学和质量控制等各个领域都特别有用，因为研究人员常常需要评估他们的样本数据是否提供了足够的证据来支持关于总体的特定主张。要执行单样本检验，首先必须制定一个原假设（H0）和一个备择假设（H1）。原假设通常声明样本均值与总体均值之间没有显著差异，而备择假设则表明存在差异。例如，如果研究人员想要检验一组学生的平均身高是否与全国平均水平170厘米不同，他们将相应地设置假设。接下来，研究人员从样本中收集数据，并计算样本均值和标准差。利用这些信息，他们可以计算出检验统计量，这将帮助确定样本均值与总体均值在标准差上的距离。对于单样本检验，常用的检验统计量包括t统计量和z统计量，具体取决于样本大小以及总体标准差是否已知。一旦计算出检验统计量，研究人员就可以将其与适当统计分布中的临界值进行比较，以决定是拒绝还是未拒绝原假设。如果检验统计量落入临界区域，则拒绝原假设，表明样本均值与总体均值之间存在统计显著差异。相反，如果检验统计量不落入临界区域，则原假设保持接受，表明不存在显著差异。此外，在执行单样本检验时考虑显著性水平（alpha）也至关重要。显著性水平代表在原假设实际上为真时拒绝原假设的概率。常见的alpha选择是0.05，这意味着有5%的风险得出结论认为存在差异，而实际上并不存在。理解这一水平的含义对于研究人员避免基于数据做出错误结论至关重要。总之，单样本检验是一种强大的统计工具，使研究人员能够根据样本数据做出有关总体参数的明智决策。通过仔细制定假设、计算检验统计量和解释结果，研究人员可以得出有意义的结论，推动各自领域的发展。无论是在学术研究、医学研究还是工业应用中，掌握单样本检验对于任何希望利用统计学进行明智决策的人来说都是必不可少的。