本次代写主要为统计相关的assignment
问题 1（23 分）
Stan 和 Berend 都种苹果。他们在同一个农贸市场上
正在对他们的苹果的甜味做出大胆的声明。作为客户在
见证争议的市场 您决定通过测试帮助他们解决争议
他们的主张。假设苹果的甜度呈正态分布
贝伦德和斯坦。
首先你要看看斯坦的苹果。幸运的是另一个观察者转身
成为一名拥有建立苹果甜度标准的装置的化学家
斯坦和贝伦德都认为这是一个客观的衡量标准。使用测试
你观察到斯坦的 12 个苹果的平均甜度为 28.6 和一个样本标准
偏差为 6.8。
在您到达之前对 Berend 苹果的样本平均值进行了分析，并且
Stan 和 Berend 知道 Berend 样本的样本均值。测试前
两个苹果样品的甜度是否有差异，Stan
讲述了他对通灵者的访问，这已经告诉他标准
他的苹果甜度的偏差是 6.8。消除不必要的噪音
他建议以样本标准差6.8为真标准
偏差。
问题 1a，5 分 论证，利用斯坦提出他的
心理故事，他想把标准差当作给定的，
你是否可以谈谈 Berend 苹果的样本均值
与斯坦苹果的样本平均值相比。
你决定无视斯坦荒谬的主张。为了惹恼斯坦，你决定
考虑 Berend 的新样本。你画了一个 18 个苹果的新样本
对于 Berend，样本均值为 29.5，样本标准差为
3.6.斯坦想通过说些聪明的话来赎回自己，并提议
假设样本的方差相等以使生活更轻松。问题 1b，6 分 在什么意义上假设 s = b，
其中 s 和 b 代表苹果甜度的标准偏差
分别为 Stan 和 Berend，让生活更轻松？构建一个 95%
在这个假设下的置信区间并争论为什么你的技术
使用这个假设工作。
Maartje 是第三位苹果农民，她决定加入讨论。她
声称平均甜度无关紧要，重要的是
苹果的百分比达到至少 30 的甜度水平。
使用此定义的 Stan 样本中的苹果用 ps = 0:5 表示。在贝伦德
样本这个分数由 pb = 8 给出
18 .对于 Maartje，您抽取了 20 个样本
苹果和她的甜苹果的比例是 pm = 0:8。
Question 1 (23 points)
Stan and Berend both grow apples. They are on the same farmers market and
are making bold claims regarding the sweetness of their apples. As a customer at
the market that witnesses the dispute you decide to help them settle it by testing
their claims. Assume that the sweetness of the apples is normally distributed
for both Berend and Stan.
First you are taking a look at Stan’s apples. Luckily another observant turns
out to be a chemist that has a device that constructs a norm for apple sweetness
that both Stan and Berend consider to be an objective measure. Using the test
you observe a mean sweetness of Stan’s 12 apples of 28.6 and a sample standard
deviation of 6.8.
The sample mean of Berend’s apples was analyzed before you arrived and
Stan and Berend know the sample mean of Berend’s sample. Before testing
whether there is a difference in the sweetness of the two apple samples, Stan
tells about his visit to his psychic that already told him that the standard
deviation of the sweetness of his apples is 6.8. To get rid of unnecessary noise
he proposes to take the sample standard deviation of 6.8 to be the true standard
deviation.
Question 1a, 5 points Argue, using the fact that Stan brings up his
psychic story and that he wants to take the standard deviation as given,
whether you can say something about the sample mean of Berend’s apples
compared to the sample mean of Stan’s apples.
You decide to ignore Stan’s ridiculous claims. To annoy Stan you decide to
consider a new sample for Berend. You have drawn a new sample of 18 apples
for Berend with a sample mean of 29.5 and a sample standard deviation of
3.6. Stan wants to redeem himself by saying something smart and proposes to
assume equal variances for the samples to make life easier. Question 1b, 6 points In what sense does the assumption that s = b,
where s and b represent the standard deviation of the apple sweetness
for Stan and Berend respectively, make life easier? Construct a 95 percent
confidence interval under this assumption and argue why your technique
works using this assumption.
Maartje is a third apple farmer and she decides to join the discussion. She
claims that the mean sweetness is not relevant and that it only matters what
percentage of apples reach a sweetness level of at least 30. The fraction of sweet
apples in Stan’s sample using this definition is denoted by ps = 0:5. In Berend’s
sample this fraction is given by pb = 8
18 . For Maartje you draw a sample of 20
apples and the fraction of sweet apples for her is pm = 0:8.