Researchers conducted an experiment, to see if adding racing stripes to cars make them go faster. They had two sets of randomly selected cars—those with and those without racing stripes—make laps around the same track. The average times of the two groups are being compared.
What null hypothesis should be used for the sampling distribution?
Hint
We are comparing the average times of two groups. We want to know if they are different or not.
Answer
The null hypothesis is that there is zero difference between the average times of the two groups.
(Avg. 1 – Avg. 2) = 0
Example 2
We think our favorite die is a little lop-sided. It seems to land on 6 more than we would expect. We're going to roll the die 50 times and record how many 6's we get. When we create our sampling distribution, what null hypothesis should we use?
Hint
How often should a fair die land on 6?
Answer
The null hypothesis is that the die lands on 6 about of the time.
Example 3
Simulation of a sampling distribution found a margin of error of ±4. If the sample mean from the data was 30, can we reject a null hypothesis of 35?
Hint
Does the estimate from the data fall within (the null hypothesis ± the margin of error)?
Answer
Yes, we can reject a null hypothesis of 35.
Example 4
The mean of a sample is 0.24. A simulation of the sampling distribution is run 10,000 times, and 44 of the trials have an estimate as large or larger than the observed sample mean. Can we reject the null hypothesis for α = 0.05?
Hint
The P-value is
Answer
Yes, we can reject the null hypothesis.
Example 5
What is the most likely value for the null hypothesis of this simulated sampling distribution?
of the time.
