# Hypothesis Testing with Two Samples

## Two Population Means with Known Standard Deviations

Even though this situation is not likely (knowing the population standard deviations), the following example illustrates hypothesis testing for independent means, known population standard deviations. The sampling distribution for the difference between the means is normal, and both populations must be normal. The random variable is



 . The normal distribution has the following format:
Normal distribution is


### References

Centers for Disease Control and Prevention. (2008, July 18). State-specific prevalence of obesity among adultsUnited States, 2007. MMWR, 57(28), 765768. Retrieved from http://www.cdc.gov/mmwr/preview/mmwrhtml/mm5728a1.htm
Federal Bureau of Investigation. (n.d.). Texas Crime Rates 19601012. Available at http://www.disastercenter.com/crime/txcrime.htm
Hinduja, S. (2013). Sexting Research and Gender Differences. Cyberbulling Research Center. Retrieved from http://cyberbullying.us/blog/sexting-research-and-gender-differences/
Humes, K. R., Jones, N. A., & Ramirez, R. R. (2011 March). Overview of race and Hispanic origin: 2010 (2010 Census Briefs). Washington, DC: U.S. Census Bureau. Available online at http://www.census.gov/prod/cen2010/briefs/c2010br-02.pdf
Smith, A. (2011, July 11). 35% of American adults own a smartphone. Pew Internet. Available online at http://www.pewinternet.org/~/media/Files/Reports/2011/PIP_Smartphones.pdf
Visually. (2013). Smart phone users, by the numbers. Retrieved from http://visual.ly/smart-phone-users-numbers

### Chapter Review

A hypothesis test of two population means from independent samples where the population standard deviations are known (typically approximated with the sample standard deviations) will have these characteristics:


### Formula Review

Normal distribution:
 .
Generally, 
Test statistic (z-score):

 
Generally, 
where

σ1 and σ2 are the known population standard deviations, n1 and n2 are the sample sizes, 
  and 
  are the sample means, and μ1 and μ2 are the population means.
Use the following information to answer the next five exercises. The mean speeds of fastball pitches from two different baseball pitchers are to be compared. A sample of 14 fastball pitches is measured from each pitcher. The populations have normal distributions.  shows the result. Scouters believe that Rodriguez pitches a speedier fastball.
Use the following information to answer the next five exercises. A researcher is testing the effects of plant food on plant growth. Nine plants have been given the plant food. Another nine plants have not been given the plant food. The heights of the plants are recorded after eight weeks. The populations have normal distributions. The following table is the result. The researcher thinks the food makes the plants grow taller.
Use the following information to answer the next five exercises. Two metal alloys are being considered as material for ball bearings. The mean melting point of the two alloys is to be compared. Fifteen pieces of each metal are being tested. Both populations have normal distributions. The following table is the result. It is believed that Alloy Zeta has a different melting point.

### Homework

DIRECTIONS: For each of the word problems, use a solution sheet to do the hypothesis test. The solution sheet is found in 