The professor of a large probability class randomly selected 8 students and asked the amount of time (in hours) spent for her course per week. The data are given below.
7 9 5 12 14 6 10 3
Estimate the standard error of the estimated time spent in a week for this course by the students who are taking this course (round off to first decimal place).

Question

BlackTom AI · Accepted Answer

We start by identifying the data and the quantity to estimate. The eight observed weekly times are: 7, 9, 5, 12, 14, 6, 10, 3 hours.

First, compute the sample mean: sum = 66, n = 8, so mean = 66/8 = 8.25 hours.

Next, determine the sample standard deviation s. Calculate each deviation from the mean and square it:
- (7 − 8.25)² = 1.5625
- (9 − 8.25)² = 0.5625
- (5 − 8.25)² = 10.5625
- (12 − 8.25)² = 14.0625
- (14 − 8.25)² = 33.0625
- (6 − 8.25)² = 5.0625
- (10 − 8.25)² = 3.0625
- (3 − 8.25)² = 27.5625
Sum of squared deviations = 95.5.
With n − 1 = 7, the sample variance is s² = 95.5 / 7 ≈ 13.642857, so s ≈ √13.642857 ≈ 3.693.

The standard error of the mean (the estimate of the population mean) is SE = s / √n. Here, SE ≈ 3.693 / √8. Since √8 ≈ 2.828, SE ≈ 3.693 / 2.828 ≈ 1.305.

Rounding to one decimal place as requested, the estimated standard error is about 1.3 hours.

To summarize, the small sample standard deviation combined with the sample size leads to a modest standard error around 1.3 hours, indicating the average weekly time estimate would vary by about 1.3 hours from sample to sample.

AMS 310 Section 7.1 Quiz

查看解析

登录即可查看完整答案

类似问题

位置1的问题 From a population of 500 elements, a sample of 225 elements is selected. It is known that the variance of the population is 900. The standard error of the mean is approximately 题库 1/1[input]. (Note: your answer should retain THREE decimal places.)

A population has a mean of 37 and a standard deviation of 13. A sample of size 5 is taken at random from this population. The standard error of the sample mean equals (up to three decimal places):

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

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