Statistics · Guided Practice
Mixed Hypothesis Tests
7 questions with answers. Try each one before revealing the answer.
1
A researcher compares the mean reaction time of professional athletes with that of amateur athletes.
State the most appropriate hypothesis test.
State the most appropriate hypothesis test.
Video solution coming soon
Answer
An independent (two-sample) t-test.
Two separate groups are being compared on a numerical mean.
Two separate groups are being compared on a numerical mean.
Video solution coming soon
2
A researcher records the memory test score of the same students in silence and again with music playing.
State the most appropriate hypothesis test, and justify your answer.
State the most appropriate hypothesis test, and justify your answer.
Video solution coming soon
Answer
A paired t-test.
The same students are measured twice, so the two sets of scores are paired.
The same students are measured twice, so the two sets of scores are paired.
Video solution coming soon
3
A biologist compares the proportion of male and female turtles that successfully migrate.
State the most appropriate hypothesis test.
State the most appropriate hypothesis test.
Video solution coming soon
Answer
A z-test for two proportions.
The data is categorical and two proportions are being compared.
The data is categorical and two proportions are being compared.
Video solution coming soon
4
A researcher investigates whether there is a relationship between hours of sleep and concentration score.
State the most appropriate hypothesis test.
State the most appropriate hypothesis test.
Video solution coming soon
Answer
A correlation test.
Two numerical variables are measured on the same individuals and the question is whether they are related.
Two numerical variables are measured on the same individuals and the question is whether they are related.
Video solution coming soon
5
Explain how you decide between a paired and an independent t-test.
Video solution coming soon
Answer
Ask whether each value in one group is naturally matched with one value in the other.
If the same subjects are measured twice, or subjects are matched in pairs, use a paired t-test. If the two groups contain different, unrelated subjects, use an independent t-test.
If the same subjects are measured twice, or subjects are matched in pairs, use a paired t-test. If the two groups contain different, unrelated subjects, use an independent t-test.
Video solution coming soon
6
A test comparing two means returns a p-value of .
Write a full conclusion at the level for a study of whether a training programme changes mean sprint time.
Write a full conclusion at the level for a study of whether a training programme changes mean sprint time.
Video solution coming soon
Answer
, so there is sufficient evidence to reject the null hypothesis at the level.
There is a significant difference in the mean sprint time before and after the training programme.
There is a significant difference in the mean sprint time before and after the training programme.
Video solution coming soon
7
Explain why the conclusion of a hypothesis test should always be written in the context of the study.
Video solution coming soon
Answer
A statement such as "reject " says nothing about the situation being investigated.
The conclusion must say what the result means for the variables in the study, so that the reader knows what has actually been shown.
The conclusion must say what the result means for the variables in the study, so that the reader knows what has actually been shown.
Video solution coming soon