Which Test?
Dr. Livingstone thinks Baylor psychology students have a higher average GPA than the national average of psychology students' GPA. The population standard deviation is known.
(upper-tailed) one-directional one-sample z-test
Notation format of the null and alternative hypotheses for a non-directional one-sample z-test.
H0: μ1=μ2
H1: μ1≠μ2
Non-directional one-sample z-test
+/- 1.96
A soda company claims its cans contain 355 ml of soda. A random sample of 50 cans has a mean of 352 ml and a standard deviation of 5 ml. At a 0.05 significance level, should we reject the null hypothesis that the mean is 355 ml?
(zcrit = +/-1.96) Reject
A Baylor administrator is curious whether there is a difference in the happiness of a sample of Baylor freshmen (M=5.45, sd=1.02, n=300) compared to the happiness of all US college freshmen (μ=3.27).
non-directional one-sample t-test
Null hypothesis notation and sentence for a one-sample t-test where we expect Dole's bananas' to last longer than competitors' bananas.
H0: μ1≤μ2 Dole's bananas last just as long or less than competitor companies' bananas.
Lower tail one-directional one-sample z-test
-1.65
A professor believes students in her class score higher than the national average of 75 on a standardized test. A sample of 20 students has a mean score of 78 and a sample standard deviation of 6. At α = 0.01, should we reject the null hypothesis?
(tcrit=2.54) Retain or fail to reject
The TAs want to test if students' K-scores for the second exam are greater than the first exam.
Upper tailed directional dependent samples t-test
Null and alternative notation for a non-directional dependent samples t-test
H0: μ1=μ2
OR μ1-μ2=0
OR μD=0
H1: μ1≠μ2
OR μ1-μ2≠0
OR μD≠0
Non-directional one-sample t-test, a=.01, df=7
+/-3.50
A fitness coach wants to test if a new training program impacts performance. Ten athletes are tested before and after the program. The mean difference in performance is 1.5 seconds faster, with a standard deviation of 1.2 seconds. At α = 0.05, should we reject the null hypothesis?
(tcrit=+/-2.26) Reject
MacKenzie is interested in whether people experience greater awe when listening to a choir versus solo version of a Black gospel song. To test this she randomly assigns participants in a study to listen to one (solo or choir) version of a song and then measures their induced awe after listening.
(upper-tailed) one-directional independent samples t-test
Sentence for the null and alternative hypotheses for a test where we want to see if there is a difference in lab A and lab B students' liking of their TAs.
H0: There is no difference in lab A and lab B students' liking of their TAs.
H1: There is a difference in lab A and lab B students' liking of their TAs.
MacKenzie wants to compare student anxiety levels before (M=5.78, n=24) and after (M=2.35, n=24) taking an exam.
+/-2.07
When comparing students attitudes before and after playing this game, MacKenzie finds a d=1.45. Should we reject the null hypothesis?
No, the d-statistic tells us practical significance, not statistical significance.
Dr. Latendresse wants to see if there is a difference in how students performed on the first exam by lab. Lab A students had an average of 60 and lab B students had an average of 80. The standard deviation of lab A was 10 and the standard deviation of lab B was 12.
Non-directional independent samples t-test
Notation and sentence for the null and alternative hypotheses for a test where we want to see if there is a difference in lab B students' liking of their TA before and after exam 2.
H0: μ1-μ2=0 There is no difference in lab B students' liking of their TA before and after exam 2
H1: μ1-μ2≠0 There is a difference in lab B students' liking of their TA before and after exam 2
MacKenzie wants to compare exam one grades of her spring lab (M=75, n=26) and her fall lab (M=80, n=24).
+/- 2.02
A researcher compares test scores between two teaching methods. Group A (n=30) has a mean of 82, and Group B (n=28) has a mean of 78. The pooled standard deviation is 5. At α = 0.05, should we reject the null hypothesis that the means are equal?
(tcrit=+/-2.01) Reject