Hypothesis Testing with the t-test (compare means)

Introduction

Every hypothesis-testing situation begins with the statement of a hypothesis. This is a conjecture about a population parameter that may or may not be true. The first example below looks at the mean number of seeds for a given population of pumpkins split by a characteristic - the use of fertilizer. The second example looks at a sample of 500 fish pulled from a lake.

There are two types of statistical hypotheses for each situation: the null hypothesis and the alternative hypothesis. In these activities they will be abbreviated as Ho and Ha.

Ho is a statistical hypothesis that states that there is no difference between a parameter and a specific value (the true value of the parameter and the selected specific value), or that there is no difference between two parameters.

Ha is a statistical hypothesis that states the existence of a difference between a parameter and a specific value (the true value of the parameter and the selected specific value), or states that there is a difference between two parameters.

In each of the examples below. The t-test used is considered a one-sided test because the alternative hypothesis has a given direction (greater than or less than). Pumpkin Seeds T-test
The alternative hypothesis is that the mean number of seeds per pumpkin with fertilizer is greater than the pumpkin plants that did not have fertilizer. The decision made was that we fail to reject the null hypothesis.

Genetic Fish T-test The alternative hypothesis is that the mean length of the genetically altered fish is greater than the mean length of the normal fish in this lake. The capture and release method is commonly used when working with wildlife and helps us make a decision with regard to the entire population of the fish in the lake. The method of capture and release is crucial, because the t-test requires random sampling. Fish were captured at different locations in the lake. [Note that the data for this activity is based on a KC data file from which I pulled out exactly 500 fish from each group]. The decision made was to reject the null hypothesis. There is a statistically significant difference in the mean lengths.

Hot Dogs - by hand simulation / Excel simulation / TP simulation Question: If left to chance, would there be a difference in calorie content as great or greater than what is observed in the given data for 52 different brands of hot dogs? Undergraduate students made a random assignment with slips of paper. Then, they used calculators (or Excel) to calculate the means of both random groups to make their decision. Hot dog T-test Simulation - by hand Beef vs Poultry Calories - TinkerPlots with detailed steps shown Goal: Determine if there is a statistically significant difference in the mean number of calories between two types of hot dogs. Beef vs Poultry Sodium - TinkerPlots with detailed steps shown Goal: Determine if there is a statistically significant difference in the mean grams of sodium between two types of hot dogs.

Four data sets - Cicadas, Car Speed, Backpack Weight and 100 Cats - are suggested for practice. Note that the groups in these practice problems do not have the same sample size. When you create the random assignments you need to match the given situation. Be sure to measure the difference in the same direction (small to large group).

Cicadas Open the sample file Cicadas (Sample Document | Science and Nature) and simulate a t-test on the attribute Body Weight (male versus female). Make sure that you assign the cicadas to random groups of size 45 and 59 and that you measure the distance in the same direction!

Car Speed Open the sample file Car Speed (Sample Document | Social Studies) and simulate a t-test on Speed (male versus female). Be sure to write down your alternative hypothesis before simulating the test!

Backpack Weight
Open the BackpackWeight file. Your quest is to determine if there is a statistically significant difference in the packweights for the students in the lower grades versus the upper grades.

100 Cats
Oh no, not the cats again. What more can we learn about this set of cats???
GeoGebra is one of the many techologies that can be used to perform the t-test. This test is used to find the p-value.

## Hypothesis Testing with the

t-test (compare means)

Every hypothesis-testing situation begins with the statement of a hypothesis. This is a conjecture about a population parameter that may or may not be true. The first example below looks at the mean number of seeds for a given population of pumpkins split by a characteristic - the use of fertilizer. The second example looks at a sample of 500 fish pulled from a lake.IntroductionThere are two types of statistical hypotheses for each situation: the null hypothesis and the alternative hypothesis. In these activities they will be abbreviated as Ho and Ha.

Ho is a statistical hypothesis that states that there is no difference between a parameter and a specific value (the true value of the parameter and the selected specific value), or that there is no difference between two parameters.

Ha is a statistical hypothesis that states the existence of a difference between a parameter and a specific value (the true value of the parameter and the selected specific value), or states that there is a difference between two parameters.

In each of the examples below. The

t-test used is considered aone-sided testbecause the alternative hypothesis has a given direction (greater than or less than).Pumpkin Seeds T-test

The alternative hypothesis is that the mean number of seeds per pumpkin with fertilizer is greater than the pumpkin plants that did not have fertilizer. The decision made was that

we fail to reject the null hypothesis.Genetic Fish T-test

The alternative hypothesis is that the mean length of the genetically altered fish is greater than the mean length of the normal fish in this lake. The capture and release method is commonly used when working with wildlife and helps us make a decision with regard to the entire population of the fish in the lake. The method of capture and release is crucial, because the t-test requires random sampling. Fish were captured at different locations in the lake. [Note that the data for this activity is based on a KC data file from which I pulled out exactly 500 fish from each group]. The decision made was to

reject the null hypothesis. There is a statistically significant difference in the mean lengths.Hot Dogs - by hand simulation / Excel simulation / TP simulationQuestion: If left to chance, would there be a difference in calorie content as great or greater than what is observed in the given data for 52 different brands of hot dogs?

Undergraduate students made a random assignment with slips of paper. Then, they used calculators (or Excel) to calculate the means of both random groups to make their decision. Hot dog T-test Simulation - by hand

Beef vs Poultry Calories - TinkerPlots with detailed steps shown

Goal: Determine if there is a statistically significant difference in the mean number of calories between two types of hot dogs.

Beef vs Poultry Sodium - TinkerPlots with detailed steps shown

Goal: Determine if there is a statistically significant difference in the mean grams of sodium between two types of hot dogs.

## Hypothesis Testing Practice Problems

Four data sets - Cicadas, Car Speed, Backpack Weight and 100 Cats - are suggested for practice. Note that the groups in these practice problems do not have the same sample size. When you create the random assignments you need to match the given situation. Be sure to measure the difference in the same direction (small to large group).CicadasOpen the sample file

Cicadas(Sample Document | Science and Nature) and simulate at-test on the attribute Body Weight (male versus female). Make sure that you assign the cicadas to random groups of size 45 and 59 and that you measure the distance in the same direction!Car SpeedOpen the sample file

Car Speed(Sample Document | Social Studies) and simulate at-test on Speed (male versus female). Be sure to write down your alternative hypothesis before simulating the test!Backpack WeightOpen the BackpackWeight file. Your quest is to determine if there is a statistically significant difference in the packweights for the students in the lower grades versus the upper grades.

100 CatsOh no, not the cats again. What more can we learn about this set of cats???

GeoGebra is one of the many techologies that can be used to perform the t-test. This test is used to find the p-value.