Question

Here are the final marks of two separate cohorts of students undertaking an intelligence test (100 is intelligent).Student Scores

Cohort A

5

10

40

50

25

70

5

95

Cohort B

45

40

55

60

50

55

75

20

Mean A: 37.5

Mean B: 50.0

SY cohort A: 7550

SY cohort B: 1800

Variance cohort A: 1078.57

Variance cohort B: 257.14

(a) If you were fitting those data to bell shaped probability curve(s), what would the curve(s) look like?

(b) What does the null hypothesis say about these two cohorts?

(c) Should I use an unpaired t-test, a paired t-test, a t-test that assumes equal variances or a t- test that doesn't assume equal variances to compare the data??

(d) If we were to compare the means of the two data sets and P was found to be less than 0.05, what would it mean?

(e) If the means of the populations are not significantly different, does it mean that the populations are the same? Why?

Answer 1

(a) The curves would look like a Normal distribution.

(b) The null hypothesis says that there is no difference betwee the mean scores of cohort A and cohort B .

(c) Since, there are two different groups (cohort A and cohort B) unpaired t- test should be used. Also the difference between the two variances is very high, so unpaired t-test that does not assume equal variances should be used to compare the data.

(d) P-value less than 0.05 means the probability of having no difference between the two means is very less, so we should reject the null hypothesis.

(e) Yes, it means that the two populations have similar parameters resulting similar distribution properties.