Calculate The Standard Error Term:

Sample Size Group 1 = 19
Sample Size Group 2 = 16
Standard Deviation Group 1 = 4.2
Standard Deviation Group 2 = 5.5
Sample Mean Group 1 = 41.9
Sample Mean Group 2 = 43.5

Question

Calculate The Standard Error Term:

Sample Size Group 1  =  19
Sample Size Group 2 = 16 
Standard Deviation Group 1  = 4.2
Standard Deviation Group 2 = 5.5
Sample Mean Group 1 = 41.9
Sample Mean Group 2 = 43.5

BlackTom AI · Accepted Answer

Restate the problem in my own words to focus the task: we need the standard error term for the difference between two sample means given the sample sizes, standard deviations, and means for Group 1 and Group 2.

First, identify the formula for the standard error of the difference between two independent means. When comparing two independent samples, the standard error (SE) of the difference in means is SE = sqrt( (s1^2 / n1) + (s2^2 / n2) ), where s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Next, compute each component step by step:
- For Group 1: s1 = 4.2, n1 = 19. The variance component is s1^2 / n1 = (4.2)^2 / 19 = 17.64 / 19 ≈ 0.9284.
- For Group 2: s2 = 5.5, n2 = 16. The variance component is s2^2 / n2 = (5.5)^2 / 16 = 30.25 / 16 = 1.890625.

Now add the two variance components to get the variance of the difference in means: 0.9284 + 1.890625 ≈ 2.8190.

Finally, take the square root to obtain the standard error: SE = sqrt(2.8190) ≈ 1.6797.

Rounding considerations depend on the required precision; at two decimal places this is approximately 1.68. The means themselves (41.9 and 43.5) are not directly used in this SE calculation, since SE concerns variability around the difference in means, not the difference in observed means themselves.

To check for consistency, ensure each component is computed with the given n and s values, and verify the arithmetic: 17.64/19 ≈ 0.9284, 30.25/16 = 1.890625, sum ≈ 2.8190, sqrt ≈ 1.6797, which rounds to 1.68 when needed.

Research Methods and Statistics in Psychology (1003PSY_3255)

Calculate The Standard Error Term: Sample Size Group 1 = 19 Sample Size Group 2 = 16 Standard Deviation Group 1 = 4.2 Standard Deviation Group 2 = 5.5 Sample Mean Group 1 = 41.9 Sample Mean Group 2 = 43.5

查看解析

登录即可查看完整答案

类似问题

Salary information regarding two independent random samples of male and female employees of a large company is shown below. Male Female Sample size 64 99 Sample mean salary (in $1000s) 440 410 Population variance 888 999 The standard error for the difference between the two means is _____.

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