Conclusions
In a hypothesis test, the p-value is 0.03 and the significance level is α = 0.05.
Should you reject or fail to reject the null hypothesis?
reject
A teacher runs a paired t-test comparing Exam 2 and Exam 3 scores for 15 students.
What are the degrees of freedom for this paired t-test?
14
A teacher wants to know whether the average score on Exam 3 for this year’s students is different from 80.
What is a one-sample t-test?
This assumption requires that your sample represents the population and was selected in a way that avoids bias.
What is the random sample assumption?
A sample has n = 20. What are the degrees of freedom for a one-sample t-test?
What is 19?
In a hypothesis test, the test statistic was t = –2.34 and the critical value was ±2.042.
Should you reject or fail to reject the null hypothesis?
Reject the null hypothesis
A one-sample t-test is conducted with a sample size of 11 at α = 0.05, two-tailed.
What is the critical t-value for this test?
2.228
A teacher records each student’s Exam 2 score and Exam 3 score and wants to determine whether there is a significant difference in performance between the two exams.
What is a paired t-test?
For a paired t-test, this assumption states that the differences you compute act like independent observations.
What is the independence of differences assumption?
Pick the Test
Clue:
A teacher wants to know whether students' stress levels changed before and after finals week using the same group of students.
What is a paired t-test?
A hypothesis test resulted in the conclusion “fail to reject the null hypothesis.”
Was the p-value less than 0.05 or greater than 0.05?
greater than 0.05
A sample has a mean of 50 and a standard deviation of 8, based on 25 observations.
What is the standard error of the mean?
1.6
A school counselor wants to compare this year’s Exam 2 average to last year’s Exam 2 average to see if scores improved.
The two groups are different students.
What is neither?
(This is a two-sample t-test, which we have not covered yet.)
Both one-sample and paired t-tests require this assumption about the distribution of data (or differences) when sample sizes are small.
What is the normality assumption (the sample data or differences are approximately normal)?
Which assumption must be met in both one-sample and paired t-tests to justify using the t-distribution for small samples?
What is the normality (of the population or of the differences) assumption?
A paired t-test was performed with a sample size of 11 students.
The test statistic was t = 2.11.
determine whether the p-value is less than 0.05 or greater than 0.05.
greater than 0.05
A teacher tests whether the average score is different from 50.
In a sample of 16 students, the sample mean is 52 with standard deviation 6.
What is the t-statistic for testing H0:μ=50?
1.33
A researcher measures students’ resting heart rate before drinking an energy drink and again after drinking it, and wants to know if the energy drink caused a change.
What is a paired t-test?
This assumption is required for a one-sample t-test, meaning each observation should not influence the value of another observation.
What is the independent observations assumption?
In a hypothesis test, the p-value is 0.014 and α = 0.05. What is the correct decision?
What is reject the null hypothesis?
A paired t-test was used to determine whether a new drug caused a significant change in patients’ blood pressure.
The test produced a test statistic of t=2.09t = 2.09t=2.09, and the conclusion was that there was a significant difference in blood pressure at the α = 0.05 (two-tailed) level.
What is the smallest sample size this result could have come from?
n=21
A sample of 25 students has a mean score of 73 with standard deviation 10.
Construct a 95% confidence interval for the true mean score, assuming a one-sample t-interval.
What is approximately (68.9, 77.1)?
A math department wants to know if the standard deviation of quiz scores this year is different from the historical standard deviation of 5 points.
What is neither?
(This would require a chi-square test for variance, not covered in our course.)
Both the one-sample t-test and the paired t-test require this condition about how the data were collected, ensuring that the observations (or the paired differences) do not systematically influence each other.
What is the independence assumption?
A paired t-test produced t = 2.48 with df = 12, and the critical value for a two-tailed test at α = 0.05 is ±2.179.
Based on this information, what is the correct conclusion?
What is: Reject the null hypothesis because the test statistic exceeds the critical value in magnitude?