Single-sample t-test & Confidence Interval – Excel & StatCrunch
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.Single-sample t-test & Confidence Interval – Excel & StatCrunch
Recognizing problem types: Hypothesis tests
Read the problem looking for keywords and values:
- What type of variable is the focus of the problem? Is it quantitative, e.g. a mean, or categorical, e.g. a proportion or percent?
- How many variables are of concern?
- Is(are) the population(s) standard deviation, sigma, given?
- Are sample variances equal or are you instructed to assume they are equal?
- What is(are) the sample size(s)?
- Is a claim or proposition mentioned?
- Are you given summary statistics or raw data?
Example 1:
At many golf clubs, a teaching professional provides a free 10-minute lesson to new customers. A golf magazine reports that golf facilities that provide these free lessons gain, on average, $2100 in green fees, lessons, or equipment expenditures. A teaching professional believes that the average gain exceeds 2,100, and collects data (shown below in the solution examples) on the gain from 15 clubs in his area. At the 0.05 level of significance, does the data support the claim?
What should you glean from reading the problem statement?Recognizing problem types: Hypothesis tests
Setting up Hypothesis Tests
The Null and Alternative
The most common problem I noticed on this assignment was caused by failing to properly identify the appropriate null and alternative hypotheses. In part, this is due to the Evans text’s somewhat confusing explanation of how to do this – the “burden of proof” approach. There is a much simpler approach that always works.
First, make sure you closely read the problem statement looking for key words and phrases. This table may help:
The null hypothesis always Setting up Hypothesis Tests
