Formulating a Hypothesis

It’s Science!

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

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)

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.

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.

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

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

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?

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

Formulate a Hypothesis for your Research…..

Questions?