# 统计代写|假设检验代写hypothesis testing代考|MATH214

## 统计代写|假设检验代写hypothesis testing代考|Z-tests versus t-tests

Z-tests are very similar to t-tests. You use both kinds of tests for the same reasons-comparing means. Both types of tests have one-sample, two-sample, and paired versions. They even have the same assumptions-with one major exception. That difference determines when you’ll use a Z-test versus t-test.

• Z-test: Use when you know the population standard deviation.
• t-Test: Use when you have an estimate of the population standard deviation.

I’m not covering Z-tests in this book for one excellent reason. You’ll never use one in practice!

Think about it. The Z-test assumes that you know the population standard deviation. That rarely happens. In what situation would you not know the population mean (hence, the need to test it), but yet you do know the population standard deviation? As I discussed earlier, these parameters are generally unknowable.

Despite this critical limitation, many statistics students learn about Ztests. Why is that? Many statistics textbooks use Z-tests because it is easier for students to calculate manually. However, the t-test is more accurate, particularly for smaller sample sizes. For more information about manually calculating Z-scores and using them to calculate probabilities, read my Introduction to Statistics ebook.

Z-tests use the standard normal distribution (mean $=0$, standard deviation $=1$ ) to calculate $\mathrm{p}$-values while $\mathrm{t}$-tests use the $\mathrm{t}$-distribution. However, the t-distribution can approximate the normal distribution.
When statisticians say that a particular distribution approximates the normal distribution, it simply means that they have very similar shapes under certain conditions. T-distributions with at least 30 degrees of freedom will closely follow the normal distribution, as shown in the probability plot below. Using either of these distributions to calculate p-values will produce similar results.

## 统计代写|假设检验代写hypothesis testing代考|Review and Next Steps

Hypothesis testing uses sampling distributions to calculate probabilities related to our data under the assumption that the null hypothesis is true. If the probability is low, our data are unlikely assuming the null is true. When the p-value is less than the significance level, our data is sufficiently incompatible with the null hypothesis that we can reject it. Our results are statistically significant, which indicates that our data favor the alternative hypothesis.

A critical aspect to remember is that $\mathrm{t}$-distributions assume the null hypothesis is correct. In turn, p-values also follow that same assumption because they come from the t-distribution. Those principles apply to the distributions, and the resultant p-values, that other hypothesis tests use. Most people get tripped up and misinterpret pvalues because they do not understand that p-values assume the null is true.

The next chapter focuses on interpreting p-values. I know what you’re thinking. We already covered them. If the $\mathrm{p}$-value is low, the null must go! And, you saw how they come from probability distributions.
However, that’s just the outcome of the hypothesis test. There is an interpretation of the specific value itself. If you can keep the sampling distributions for the test statistic and its assumption of a true null hypothesis in mind, you’ll have an advantage for understanding how to interpret p-values correctly!

# 假设检验代考

## 统计代写|假设检验代写hypothesis testing代考|Z-tests versus t-tests

Z 检验与 t 检验非常相似。您出于相同的原因使用这两种测试 – 比较方法。两种类型的测试都有单样本、双样本和配对版本。他们甚至有相同的假设——只有一个主要例外。这种差异决定了您何时使用 Z 检验与 t 检验。

• Z 检验：当您知道总体标准差时使用。
• t 检验：当您估计总体标准差时使用。

Z 检验使用标准正态分布（均值=0, 标准偏差=1） 计算p-值同时吨-测试使用吨-分配。但是，t 分布可以近似于正态分布。

## 统计代写|假设检验代写hypothesis testing代考|Review and Next Steps

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