## Posts filed under ‘StatCrunch’

### Setting Up Binomial and Poisson Probability Problems

I have uploaded 2 videos to YouTube that go over how to set up binomial and Poisson probability problems. (There are 8 binomial problems, and 6 Poisson problems.) I go over the steps for identifying the problems, as well as give the correct answers. If you’d like a copy of the actual problems, just drop me a line.

- George

I am a math instructor at College of the Sequoias in Visalia, CA. If there’s a particular topic you’d like me to address, or if you have a question or a comment, please let me know. You can reach me through the contact page on my website – http://georgewoodbury.com.

### StatCrunch – Binomial Probability Calculator

I just finished up a short unit on binomial probabilities with my Intro Stat class, using StatCrunch as the primary method of calculating probabilities. To access the calculator in StatCrunch, click the Stat button, and select Binomial from the Calculator option.

Here is the interface.

Enter the number of trials in the box labeled n and the probability of success on one trial in the box labeled p. When it comes to the number of successes, you have several options: <= (for $\le$), => (for $\ge$), <, >, or =. Enter the appropriate value for x once you have selected the option you need and press Compute.

By the way, if you need to find something like $P(3 \le x \le 7)$, you will have to do it in 2 steps. (StatCrunch does not have a “between 3 & 7″ option.) First, find $P(x \le 7)$, and then subtract the result you get from $P(x<3)$.

One of the features I like is the graphical display of the probabilities. The values of x that you are working with are displayed with red bars.

By making the actual calculations easier, I find that we can spend more time on challenging problems. My students also have a better understanding of the big picture, instead of getting lost in the weeds with their calculators and 20 pages of binomial probability tables.

- George

I am a math instructor at College of the Sequoias in Visalia, CA. If there’s a particular topic you’d like me to address, or if you have a question or a comment, please let me know. You can reach me through the contact page on my website – http://georgewoodbury.com.

### Intro Stats – Sampling Techniques Activity

During the first week of class I go over different sampling techniques – Convenience, Random, Systematic, Cluster, & Stratified. Even though most of our sampling during the semester will be convenience sampling, I think it’s important for students to understand the other types that are available. It gives me a chance to talk about what I feel is one of the major themes of statistics, the tradeoff between easy/less reliable and difficult/more reliable. Basically we are looking for a practical approach that yields quality results.

I use Mike Sullivan’s Intro Stats text, and yesterday I used one of his activities to show the different sampling techniques in action. I asked my students two questions. How much did you spend this semester on books and supplies? Do you own an iPhone? We had two variables, one quantitative and one qualitative. I told the students that through sampling techniques we would try to estimate the mean cost for students in this class as well as the percentage of students in this class that own an iPhone.

Random Sampling

I began by numbering the students from 1 through 44. I then used Microsoft Excel to select random numbers until we had a sample of 10 students, wrote the data for those students on the board, and we calculated the sample mean and proportion.

Systematic Sampling

Students struggle with systematic sampling in the homework because they are given an abstract situation, asked to calculate a step value, and give the number of the 47th individual selected. It is more effective to show systematic sampling by actually taking a sample. We had 44 students and I wanted a sample size of 10, so my students told me that a step size of 4 would work. (44/10) We randomly selected a starting value using Excel, and then sampled every 4 students from there. Students started to understand that this was pretty similar to the way we used to count off in gym class to pick teams. Once I had the data on the board, we calculated the sample mean and proportion.

Cluster Sampling

I have 6 rows of tables in my classroom, so we made each row a cluster. We selected a row at random (Excel) and sampled each individual in that row. In my experience students do pretty well with the idea that cluster sampling can be done by dividing the population geographically by location and sampling each individual in the selected clusters. Again, once the data was on the board we calculated the sample mean and proportion.

Stratified Sampling

I began by asking my students which strata we could use to categorize students, and they came up with gender pretty quickly. It is pretty easy to use gender as opposed to year in school, religious affiliation, … because it is information we already know. I took a sample of 6 female students and 3 male students, as my class roughly has a 2:1 ratio of females to males. We renumbered students within each group and used Excel to randomly select students. Once the data was on the board we calculated the sample mean and proportion.

Wrap Up

Once we were done sampling I collected all of the information for the entire class and calculated the population mean (~ $315) and proportion (~38%). We then compared our sample statistics to the population parameters, and the students really got to see that individual samples vary. This is a really BIG idea as we head towards inferential statistics. I feel that my students got a much better handle on sampling techniques and on sampling in general. Next week I will show them how to use StatCrunch to draw a random sample. Do you have any sampling activities that you use and really like? Or any other activities that you’d like to share? Leave a comment or drop me a line – maybe we can arrange a guest blog! - George I am a math instructor at College of the Sequoias in Visalia, CA. If there’s a particular topic you’d like me to address, or if you have a question or a comment, please let me know. You can reach me through the contact page on my website – http://georgewoodbury.com. ### Hypothesis Test – Single Proportion (p-value) In this blog I will go over the steps for performing a hypothesis test for a single population proportion. I will use the p-value approach, and give directions for using StatCrunch. Example: A physician claims that more than 10% of pregnant women smoke while pregnant. A survey of 400 randomly selected pregnant women revealed that 60 of them smoked while pregnant. Test the physician’s claim at the 0.05 level of significance. This is a one-proportion test because the claim compares a single population proportion (the proportion of all pregnant women who smoke) to a certain number (10%). In addition we have one set of sample information of the form x out of n (60 out of 400). Step 1 Since the claim is that the proportion of all pregnant women who smoke is above 10%, this tells us that the hypotheses for this test are: $H_0: p=0.10\\ H_1: p>0.10$ Step 2 The level of significance stated in the problem is $\alpha=0.05$. If the p-value is less that 0.05, this is sufficient sample evidence to reject the null hypothesis. Step 3 The appropriate test statistic for the one-proportion hypothesis test is $z=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}$. This formula is used to calculate a z-value associated with the sample data, which is in turn used to determine the p-value for the test. Step 4 The decision rule for this test is to reject $H_0$ if the p-value is less than 0.05. When using the p-value approach, the decision rule is always to reject $H_0$ is &latex p-value<\alpha}$.

Step 5

In StatCrunch, begin by following Stat > Proportions > One sample > with summary.
Enter the sample information for the number of successes (60) and the number of observations (400). Click the “Next” button.
The hypothesis testing option should be active. In the box for the null hypothesis, change the proportion to 0.10, and change the option for the alternate hypothesis to “>”. Click the “Calculate” button.

Here is the output from StatCrunch:

The value of the test statistic is $z=3.33$. (You could calculate this with a calculator using the formula in step 3.)

The p-value for this test is 0.0004. (You could determine this by finding the area under the normal curve to the right of $z=3.33$.)

Since the p-value is less than 0.05, we reject $H_0$. This supports the physician’s claim that more than 10% of all pregnant women smoke.

Summary

I hope that you find this useful. In future blogs I will explain how to use StatCrunch to perform other hypothesis tests. If you have any StatCrunch or statistical questions, you can reach me through the contact page on my website .

-George

I am a mathematics instructor at College of the Sequoias in Visalia, CA. Each Friday I often blog about technology (including StatCrunch), inside and outside of the classroom. Let me know if there are other topics you’d like me to cover by leaving a comment or by reaching me through the contact page on my website: georgewoodbury.com.

### StatCrunch – Hypothesis Tests For A Population Mean

In today’s blog I will go over the steps for performing a hypothesis test for a single population mean using StatCrunch. Although I will be explaining the p-value approach to these tests, you could also use StatCrunch for a classical hypothesis test.

I will be focusing on both the z-test and the t-test for a single population mean. Consult your instructor, class notes, and/or textbook for the conditions for determining when to use a z-test and when to use a t-test.

z-test if you have summary data …

If you want to perform a z-test and already know the sample mean, sample standard deviation, and sample size, click the “Stat” button in StatCrunch and select “Z statistics” > “One sample” > “with summary” from the menu list. When the dialog box opens, input the sample mean, sample standard deviation, and sample size in the appropriate boxes.

Click the “Next” button to go to the second screen. Here you need to determine the inequality sign for the alternate hypothesis as well as the claimed value of $\mu$. Click on the “Calculate” button to display the results.

Here is the output box showing the results for testing $H_0: \mu = 55.8$ versus $H_1: \mu > 55.8$ with a sample mean of 57, a sample standard deviation of 6.2, and a sample size of 123.

In addition to calculating the Z-Statistic, StatCrunch provides you with the p-value for the test. Here the p-value is 0.0159. Here is how the hypothesis test would be written at $\alpha = 0.05$.

Step 1

$H_0: \mu = 55.8 \\ H_1: \mu > 55.8$

Step 2

$\alpha = 0.05$

Step 3

One mean, z-test

$\frac {\bar {x} - \mu}{s/ \sqrt {n}}$

Step 4

Reject $H_0$ if p-value < 0.05.

Step 5

p-value = 0.0159

Reject $H_0$.

There is significant evidence to support $H_1$.

z-test if you have sample data …

If you have sample data to work with, begin by typing it in one column in the StatCrunch spreadsheet. (Sample data can be copied and pasted into StatCrunch from other programs.) To perform the test, start with the “Stat” button and select “Z statistics” > “One sample” > “with data” from the menu list.

On the first screen of the dialog box you bill be prompted for the column containing the data, as well as the population standard deviation. On the second screen, enter the inequality for the alternate hypothesis as well as the claimed value of $\mu$ and click the “Calculate” button.

The output is displayed in the same fashion as the test “with summary” as shown above.

t-tests

If you need to perform a t-test, use the “T statistics” button.

The test “with summary” is exactly as it is described above for the z-test.

The test “with data” is the same as the z-test above, except you will not need to enter the (unknown) population standard deviation.

Summary

I hope that you find this useful. In future blogs I will explain how to use StatCrunch to perform proportion tests, 2-sample tests, chi-square tests, ANOVA, and paired sample tests. If you have any StatCrunch or statistical questions, you can reach me through the contact page on my website .

-George

I am a mathematics instructor at College of the Sequoias in Visalia, CA. Each Friday I will blog about technology, inside and outside of the classroom. Let me know if there are other topics you’d like me to cover by leaving a comment or by reaching me through the contact page on my website: georgewoodbury.com.

### StatCrunch Group Features

All of my previous StatCrunch posts have focused on the StatCrunch tool, which is fantastic. Today I’ll talk about StatCrunch groups and how they can enhance your class.

You can create a group for your class to join. This allows you to easily share a survey for your students to take, share the results, or share any other data set you wish.

Your students can do the same – they can post their own survey and share data sets. They can also publish their own StatCrunch results, which is a terrific way to “turn in” homework. The instructor, and other students, can post comments on student work. It is close to Facebook for the statistics classroom – an easy way for students to post work for others to examine.

This feature is only available with the full blown StatCrunch access, which now comes automatically for students who enroll in a MyStatLab course.

If you have any questions or comments about StatCrunch, I invite you to share your thoughts – please leave your comment or you can reach me through the contact page on my website .

-George

I am a mathematics instructor at College of the Sequoias in Visalia, CA. Each Friday I will blog about technology, inside and outside of the classroom. Let me know if there are other topics you’d like me to cover by leaving a comment or by reaching me through the contact page on my website.

### Starting With StatCrunch

There are a few approaches to using StatCrunch in your intro stats course that my colleagues and I use. They are all pretty effective, it probably depends more on your teaching style and the physical set up of your classroom.

My Approach

I teach in a smart classroom, so I have a computer with Internet access and a projector. Each day, I try to stop lecturing 5-10 minutes before the end of class and then demonstrate how we can use StatCrunch with that day’s material. StatCrunch is so intuitive to use that students can understand the procedures with minimal notes. This improves as the semester progresses as well.

I encourage my students to use StatCrunch to help solve textbook exercises as well as while working on their MyStatLab homework. I do not collect required StatCrunch work on a section by section basis, but instead assign one assignment per exam that I call a “Test Supplement”. The idea of these assignments is to use StatCrunch tools to demonstrate that students understand the underlying statistical concepts. For example, for the first Test Supplement I give students two sets of test scores and ask them to use numerical and graphical measures to describe each set. Then students have to take their results and use them to support an essay that states that one version of the test was harder than the other or that the two tests were of equal difficulty.

Another Approach

One of my colleagues also demonstrates StatCrunch on a daily basis, but collects a short task-driven lab each week. A benefit to this approach is that he is sure his students are using StatCrunch on a regular basis.

A Third Approach

Another colleague does not discuss StatCrunch in class. As the midterm approaches he gives out a packet with step by step directions for statistical procedures, and then has a comprehensive assignment for his students. One benefit to this approach is that it really helps students to review topics as the midterm approaches. (He has a similar packet/assignment for the inferential portion of the course.)

Collecting Work

By the way, it is quite easy to collect StatCrunch work from students. Students can copy their results and paste them into a Word document or an email and send them to you or drop them in a digital dropbox. Now that the full version of StatCrunch is tied to MyStatLab students can post their work for you to view.

Summary

If you have any questions or comments about StatCrunch, I invite you to share your thoughts – please leave your comment or you can reach me through the contact page on my website .

-George

I am a mathematics instructor at College of the Sequoias in Visalia, CA. Each Friday I will blog about technology, inside and outside of the classroom. Let me know if there are other topics you’d like me to cover by leaving a comment or by reaching me through the contact page on my website.

For those of you who use MyStatLab and/or StatCrunch, this semester marks the beginning of the dual log in. Students who create a MyStatLab account will receive full access to StatCrunch. This means that your students will be able to not only use the power of StatCrunch to increase their understanding of statistics, they will also be able to

• post their own polls to gather data
• easily access data posted by their instructor
• post their results for others to see

I give this move 2 thumbs up and can’t wait to use it in my classes.

-George

I am a math instructor at College of the Sequoias in Visalia, CA. Each Friday I will be blogging about technology, including StatCrunch. If there’s a particular topic you’d like me to address, or if you have a question or a comment, please let me know. You can reach me through the contact page on my website – http://georgewoodbury.com.

### Intro Stats Final Exam Using StatCrunch

Last week I gave my final exam using StatCrunch, and I’m quite pleased with the results.

### Overcoming Anxiety

I was a little nervous about this exam. Will there be enough time? What if we lose power? What if my students are not as prepared as I think?

Our college schedules 2-hour final exams. My exam was made up of 10 problems – 2 confidence intervals and 8 hypothesis tests – and time ended up not being an issue. Most students took approximately 1 hour to complete the exam.

My contingency plan for power loss was to provide students with p-values for each test, essentially I would take the role of StatCrunch. Not ideal, but my students could take my information and complete their exam.

My students, as a group, were well prepared.

• One class had 31 students take the exam, and they all passed. There were 18 A’s, 10 B’s, and 3 C’s. The median score was 93.
• The other class had 39 students take the exam, and 32 passed the exam. There were 21 A’s, 9 B’s, 2 C’s, 2 D’s, and 5 F’s (47, 44, 22, 22, 10). The median score was 91. The students who earned F’s had been performing poorly heading into the exam, and as a rule struggled with identifying the appropriate test and writing up the 5 step hypothesis test.

### Format of the Exam

As I mentioned earlier, there were 2 confidence intervals and 8 hypothesis tests. We had covered 3 confidence intervals (one mean z, one mean t, and one proportion) and 10 hypothesis tests (one mean z, one mean t, one proportion, paired difference, two mean, two proportion, two variance, goodness of fit, chi square independence, ANOVA). Some of the problems provided summary data, while others provided raw data.

For confidence interval problems, students had to explain exactly what the confidence interval told them in their own words.

For hypothesis test problems, students had to write up a 5 step hypothesis test.

1. H0 and H1, as well as H1 in words
2. Level of significance
3. Test being performed
4. Decision rule (p-value approach)
5. Test stat and p-value from StatCrunch, Decision about H0, Conclusion about H1

There were also follow up questions after each test. Examples include “Is this a z-test or a t-test? Explain your answer fully.”, “Do your results prove that the mean for City A is greater than the other 3 cities? (ANOVA)”, “Do your results prove that 75% of working mothers purchase take-out food each week?”

To answer these questions, students need to completely understand the hypothesis testing procedure and exactly what each test is testing. For instance, students need to understand that we either reject or fail to reject H0, we never support that statement. Students need to understand whether two variables are related based on the chi-square goodness of fit test.

As I graded their exams, I was relieved that the students were successful in identifying the proper test and getting the correct results from StatCrunch. But what made me smile was that they were so successful with my follow up questions.

### Summary

I am so pleased with my use of StatCrunch! I plan to take another giant step when I teach this course again. In the early part of the course, I will spend less time on calculation and more time on interpretation and big picture ideas. I will fully incorporate the probability distribution calculators rather than relying on formulas and tables. I will teach confidence intervals with each hypothesis test. And I will cover more hypothesis tests and regression.

Do you use StatCrunch, or some similar technological tool, in your statistics courses? Would you like to share your approach, and particularly your exam strategies, with other instructors? Do you have any questions on StatCrunch? Would you like a copy of my exam? If so, please leave a comment or reach me through the contact page at my web site – georgewoodbury.com.

-George

I am a math instructor at College of the Sequoias in Visalia, CA. If there’s a particular topic you’d like me to address, or if you have a question or a comment, please let me know. You can reach me through the contact page on my website – http://georgewoodbury.com.

### Using StatCrunch For A Final Exam

This semester I am giving my Intro Stats final exam in a computer lab. The exam is completely inferential covering confidence intervals and 10 hypothesis tests – 1 mean z, 1 mean t, 1 proportion, paired difference, 2 mean, 2 proportion, 2 variance, goodness of fit, chi-square independence, and ANOVA.

My students will be using StatCrunch to generate confidence intervals and p-values. On the last day of class I allowed my students to create a “StatCrunch cheat sheet”. They were able to write down important steps for finding the appropriate test in the StatCrunch menus, as well as important facts to remember for particular tests such as remembering to uncheck the Pool Variances option on a two mean test. I will give them these cheat sheets when they arrive to take their final.

### What I Am Testing

I’m really happy with my approach with this exam, and this course in general. Here are the skills that are being tested.

• Upon reading a problem, a student must be able to determine which statistical test is appropriate.
This skill is very valuable in their statistical future. Whether it is in a future course in their major or out in the workforce, the first step in solving a problem with statistical analysis is to determine which test is appropriate.
• A student must be able to extract all important information and enter that information into our statistical analysis package – StatCrunch.
• A student must be able to interpret the results generated through technology.
Again, this is a very important skill. Students will often find themselves in a position where data will be presented to them and they will have to interpret the results. In my experience, students will find that they will be presented others’ results more often than they will have to perform their own analysis. They must be able to read, understand, and interpret the results of others.
• A student must be able to correctly interpret a confidence interval or the results of a hypothesis test.
I ask questions that ensure that my students completely understand what they are doing rather than just mindlessly mimicking steps. It is here that I am able to focus on conceptual understanding.

### Perceived Benefits

My students have not devoted their mental energy to figuring out how to evaluate a particular formula. StatCrunch has allowed them to spend more of their energy on truly understanding the material in the course. The course is now taught in a way that has real world value.

The switch was not easy for me. Sometimes I would wonder whether this approach was valid because my students were not doing many calculations by hand. Confession – I used to have my students do ANOVA calculations by hand. This semester I showed them all of the formulas, and they were unanimous in their support of our new approach.

The final exam is next Tuesday and Wednesday. I’ll be back to share the results, as well as the results of a student satisfaction survey I’ll be giving.

Do you use StatCrunch, or some similar technological tool, in your statistics courses? Would you like to share your approach, and particularly your exam strategies, with other instructors? Do you have any questions on StatCrunch? If so, please leave a comment or reach me through the contact page at my web site – georgewoodbury.com.

-George

I am a math instructor at College of the Sequoias in Visalia, CA. One of my Thursday topics is Technology in Education, including StatCrunch. If there’s a particular topic you’d like me to address, or if you have a question or a comment, please let me know. You can reach me through the contact page on my website – http://georgewoodbury.com.