The grade point averages for 12 randomly selected students are shown in the table below. Find the 99% confidence interval around the population mean, µ. Assume the population is normally distributed.
This is a small sample, n < 30, and we do not know sigma. Although small samples generally are t-distributions, the deciding factor for BUS233 is the lack of the population standard deviation, sigma. Therefore, use the t-distribution.
The Excel solution is: [Read more…] about Single-Sample, Confidence Interval for a Mean using t-distribution
Sometimes you are confronted with a deceptively simple-looking problem:
Construct the indicated confidence interval for the population mean, µ.
c = 0.90, x-bar = 16.2, s = 5.0, n = 75.
To solve it you need to carefully inspect the data you are given. You should notice two things. You are not given the population standard deviation, σ, and the n is > 30.
Depending upon the author of your stats book (and your instructor), you will choose either the normal distribution or the t-distribution to solve it. Some authors (e.g. Larson) say if you do not know sigma, use the t-distribution. Other authors say if n > 30, it is OK to use the normal distribution with s being approximately equal to σ. (McClave, Benson, & Sincich, 2014, p 303)
When we do not know the population standard deviation sigma, σ, and the sample size, n, is less than 30, we use the t-test to evaluate a claim. Consider the following problem:
A scientist thinks the mean waste recycled by adults in the US is now more than one pound per person per day. In a random sample of 12 US adults, the mean waste recycled per day per person is 1.9 pounds with a standard deviation of 0.3 pounds. At a 10% significance level, does the sample data support the claim?
In statistics, it is always a good idea to sketch the situation described in the problem:
The sample mean is far to the right of the assumed population mean, µ = 1. [Read more…] about Single-sample t-test & Confidence Interval – Excel & StatCrunch
This post is in development. In the interim, please try out the attached Excel workbook with a couple of useful calculators
I see a lot of students struggle with recognizing what a problem statement is asking them to do. Consider this problem:
What do you get from that reading? I get: [Read more…] about Hypothesis Test for Mean Difference using StatCrunch