AP Statistics : How to establish an alternate hypothesis
Study concepts, example questions & explanations for AP Statistics
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Example Questions
Example Question #1 : How To Establish An Alternate Hypothesis
A researcher stated that 
The question states that the researcher thinks the percent of liberal Americans in 2012 is different than the 
Example Question #1 : Significance Logic And Establishing Hypotheses
The department of labor reports that umemployment is down to 5% in the United States. A politician claims that the data was manipulated to show better numbers. The politician believes our country is worse off that unemployment must be worse than the claim made by the department of labor. What is the alternative hypothesis for a test for this situation?
Ha:
Ha:
Ha:
Ho:
Ho:
Ha:
The alternative hypthesis is denoted by Ha. The alternative represents the value that is being tested for and not the original claim. The original claim for the problem is unemployment is 
Example Question #1 : How To Establish An Alternate Hypothesis
A researcher wants to determine whether there is a significant linear relationship between time spent meditating and time spent studying. What is the appropriate alternative hypothesis for this study?
This question is about a linear regression between time spent meditating and time spent studying. Therefore, the hypothesis is regarding Beta1, the slope of the line. We are testing a non-directional or bi-directional claim that the relationship is significant. A slope of zero indicates no relationship between the two variables. Therefore, the alternative hypothesis is that the slope is not equal to zero.
Example Question #1 : How To Establish An Alternate Hypothesis
A researcher wants to compare 3 different treatments to see if any of the treatments affects study time. The three treatments studied are control group, a group given vitamins, and a group given a placebo. They found that the average time spent studying with control students was 2 hours, with students given vitamins it was 3 hours, and with placebos students studied 5 hours. Which of the following is the correct alternative hypothesis?
Not all of the means are equal
Not all of the means are equal
Because we are comparing more than 2 groups, we must use an ANOVA for this problem. For an ANOVA problem, the null hypothesis is that not all of the groups’ means are the same. 
Example Question #4 : How To Establish An Alternate Hypothesis
A researcher wants to investigate the claim that taking vitamins will help a student study longer. First, the researcher collects 32 students who do not take vitamins and determines their time spent studying. Then, the 32 students are given a vitamin for 1 week. After 1 week of taking vitamins, students are again tested to determine their time spent studying. Which of the following is the correct alternative hypothesis?
Because the same students are tested twice, this is a paired study, therefore we must use a hypothesis appropriate for a paired t-test. The hypothesis for a paired t-test regards the average of the differences between before and after treatment, called 
Example Question #5 : How To Establish An Alternate Hypothesis
A study would like to determine whether meditation helps students improve focus time. They know that the average focus time of an American 4th grader is 23 minutes. They then recruit 50 meditators and calculate their average focus time. What is the appropriate alternative hypothesis for this study?
Because we are comparing one sample to a known mean, the hypothesis takes the form of 
Example Question #6 : How To Establish An Alternate Hypothesis
A study would like to determine whether meditation helps students increase focus time. They used a control group of 30 students and compared their focus time to a group of 30 meditating students and compared their average time spent meditating. What is the appropriate alternative hypothesis for this study?
Because we are comparing two samples, the hypothesis takes the form of 
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