Imagine that a researcher appropriately collects data from 83 people from a particular population for variable X. They obtain a mean of 40.3 from these 83 people. He also knows that the population mean for variable X is 49 (μ = 49) with a standard deviation of 7.3 (σ = 7.3). Using this information, compute the z statistic.

Please report the correct z statistic below with two decimal places (if relevant).

Question

Imagine that a researcher appropriately collects data from 83 people from a particular population for variable X.  They obtain a mean of 40.3 from these 83 people.  He also knows that the population mean for variable X is 49 (μ = 49) with a standard deviation of 7.3  (σ = 7.3). Using this information, compute the z statistic.

Please report the correct z statistic below with two decimal places (if relevant).

BlackTom AI · Accepted Answer

We start by identifying the formula for the z statistic in a one-sample z test when the population standard deviation is known: z = (x̄ - μ) / (σ / √n).

First, compute the standard error of the mean: SE = σ / √n = 7.3 / √83.
√83 is approximately 9.11, so SE ≈ 7.3 / 9.11 ≈ 0.801.

Next, compute the difference between the sample mean and the population mean: x̄ - μ = 40.3 - 49 = -8.7.

Now form the z statistic with these values: z = (-8.7) / 0.801 ≈ -10.86.

Rounding to two decimal places as requested, the z statistic is approximately -10.86.

Key checks:
- The sign is negative because the sample mean is below the population mean.
- The standard error is the standard deviation of the sampling distribution of the mean, which decreases with larger sample size, hence the fairly large magnitude of z given a relatively small SE.

Note: This calculation assumes that σ = 7.3 is the known population standard deviation and that a z-test is appropriate for this scenario.

查看解析

登录即可查看完整答案

类似问题

For the following hypothesis test: With n = 80, σ = 9, and = 47.1, state the calculated value of the test statistic z.

In a consumer society, many adults channel creativity into buying things

Economic stress and unpredictable times have resulted in a booming industry for self-help products

People born without creativity never can develop it

A product has a selling price of $20, a contribution margin ratio of 40% and fixed cost of $120,000. To make a profit of $30,000. The number of units that must be sold is: Type the number without $ and a comma. Eg: 20000

Which of the following statement regarding cost is correct:

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单