Formulating a Hypothesis

1. Formulating a Hypothesis It’s Science!

2. Hypothesis • A Hypothesis is an educated guess that is testable • A Hypothesis is an assumption about a population parameter • If, Then, Because (Hypothesis and Prediction) • If, The, Because, How (Hypothesis, Prediction and Methods) • www.sciencebuddies.org Definition, examples & checklist

3. The Null and Alternative Hypothesis • The Null hypothesis, denoted by H0 , represents the status quo and involves stating the belief that the mean of the population is <, =, or > a specific value. • The alternative hypothesis, denoted by H1 , represents the opposite of the null hypothesis and holds true if the null hypothesis is found to be false. (<, not =, or > a specific value)

4. Example • Let’s say that my hypothesis is that it will take an average of 6 days to capture a loose snake in a house. (population mean is = to 6 days) • Suppose after I gathered a sample of people who had snakes loose in their home and averaged the data, I found it took 6.1 days. The hypothesis test will then tell me whether or not 6.1 days is significantly different from 6 days or if the difference is merely due to chance.

5. Example Continued • H0 : µ = 6.0; µ > 6.0; µ < 6.0 • H0 : µ is not = 6.0; µ > 6.0; µ < 6.0 • Show graph of Two-tail hypothesis test (p. 217) • The curve in the figure represents the sampling distribution of the mean for the number of days to catch a snake. The mean of the population, assumed 6.0 days according to the null hypothesis, is the mean of the sampling distribution.

6. Procedure • Collect a sample size, n, and calculate the test statistic, which is usually the sample mean • Plot the sample mean on the x-axis of the sampling distribution curve • If the sample mean falls within the “Do Not Reject” region…meaning we do not have enough evidence to support the alternative hypothesis, then the null is not rejected • If the sample mean falls in either shaded region know as the “rejection regions,” then we have enough evidence to support the alternative hypothesis

7. In Conclusion • The only 2 statements that we can make about the null hypothesis are that we either reject the null hypothesis or we do not reject the null hypothesis • Since Science can never be absolutely “proven” only “disproven,” it is “safer” to reject or not reject rather than accept

8. Example Problem • Formulate a hypothesis statement for the following claim: “The average adult drinks 1.7 cups of coffee per day.” A sample of 35 adults drank an average of 1.95 cups per day. Assume the population standard deviation is 0.5 cups. Using α = 0.10, test your hypothesis. What is your conclusion?

9. Solution • H0 : µ = 1.7 cups H1 does not = 1.7 cups • n= 35 adults; σ = 0.5 cups; α=0.10 • Standard Error of the Mean: σx =σ/square root of n=0.50/square root of 35=0.0845 cups • z=mean - µ/std error of the mean; z = +or – 1.64 • Upper Limit = 1.7 + 1.64(0.0845) = 1.84 cups • Lower Limit = 1.7 – 1.64(0.0845) = 1.56 cups • Since the mean =1.95 cups, we reject the null hypothesis and conclude that the population mean is not 1.7 cups per day

10. Formulate a Hypothesis for your Research….. • Questions?