Download a PDF with the step-by-step instructions for finding the confidence interval for a population mean, μ, using StatCrunch.

# StatCrunch

## Chi-square Goodness of Fit test

Consider the following problem:

A research firm claims that the distribution of the days of the week that people are most likely to order food for delivery is different from the distribution seen in the past. You randomly select 494 people and record which day of the week each is most likely to order food for delivery. The table below also shows the results of your count. At alpha, α, = 0.05, test the research firm’s claim.

This sounds like a test of Goodness of Fit between the historical pattern and the observed pattern.

The claim is that the actual pattern and the historical pattern are different. That means we need the inequality math operator, which, in turn, means the **claim is the alternative hypothesis**.

Stating our two hypotheses: [Read more…] about Chi-square Goodness of Fit test

## Normal Distribution Problem- Two Common Mistakes

I see many students in my intro statistics courses missing problems related to the normal distribution. One especially common mistake is not using the correct “standard deviation” to find probabilities and percentiles.

Consider the following problem statement:

A bank auditor claims that credit card balances are normally distributed, with a mean of $2870 and a standard deviation of $900.

- What is the probability a randomly selected credit card holder has a card balance less than $2500?
- You randomly select 25 credit card holders. What is the probability that their mean card balance is less than $2500?
- Interpret the two probabilities in terms of the auditor’s claim.

I usually see students get one of the questions correct, but not all. And they either seem to get #1 or #2 correct in about equal proportions. When I inspect their solutions, I find that they get confused over the “standard deviation” to use in the equation for z.

Most students seem to get #1 correct. They use the formula for z: [Read more…] about Normal Distribution Problem- Two Common Mistakes

## Normal Distribution: Example Problem 1

One way to improve your ability to solve normal distribution problems is to work on recognizing what word problems are requesting you to do.

Consider the following problem statement:

In an investigation of the personality characteristics of drug dealers of a certain region, convicted drug dealers were scored on a scale that provides a quantitative measure of person’s level of need for approval and sensitivity to social situations. (Higher scores indicate a greater need for approval.) Based on the study results, it can be assumed that the scale scores for the population of convicted drug dealers of the region has a mean of 44 and a standard deviation of 7. Suppose that in a sample of 96 people from the region, the mean scale score is x̅ = 46. Is this sample likely to have been selected from the population of convicted drug dealers of the region? Explain. Consider an event with a probability less than 0.05 unlikely. (McClave, Benson, & Sincich, 2014)

Solution:

First, state the question: How unusual would it be to get a sample mean of 46 if the population mean is 44 and the population standard deviation is 7? [Read more…] about Normal Distribution: Example Problem 1

## Simple Regression Part 3

When you are given raw data on a test, solving the problem using technology is relatively simple. But when you are given intermediates or partial solutions, the task becomes a bit more difficult since most software is not set up to work on intermediates.

Consider the following problem:

A scientist employed simple linear regression to model the monthly price of recycled newspaper as a function of the monthly price of pulpwood. The results shown below were obtained for monthly data collected over a recent 10-year period (n = 120 months).

Use this information to conduct a simple linear regression analysis:

ŷ = 35.20+5.28x; for testing H_{0}: β_{1 }= 0, t = 2.45; r = 0.22; r^{2} = 0.05. [Read more…] about Simple Regression Part 3

## Single-Sample, Small Sample, Confidence Interval for a Mean

Consider the following problem:

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.

Solution:

Because this is a small sample, n < 30, and we do not know sigma, use the t-distribution.

The Excel solution is: [Read more…] about Single-Sample, Small Sample, Confidence Interval for a Mean