Question

In fall 2010, students in my 2 p.m. section of the Introduction to Biological Science I class reported their height
below on the first column of the table, while my 5 p.m. section reported their height on the second column. I
wondered: are the average heights of these two sections significantly different?
Students’ height in
Introduction to Biological
Science I courses (inches)
2 pm 5 pm
70 67
69 61
67 59
62 62
70 62
69 68
66 67
63 68
68 69
63 61
76 69
59 66
62 62
62 62
75 61
62 70
72 58
63 61
Use the data table provided and conduct your calculation on the excel sheet to answer the following questions (DO NOT
use the T.TEST or T.DIST formulas on Excel until it is requested in the questions. Use Average, STDEV, etc. to avoid
rounding error):
(1) Based on the nature of the data, you identify and determine that _____ t-test is the most appropriate test to
evaluate the difference in height between the 2pm and 5pm student populations.
Answer: ___________ (Please answer with a or b only)
a. paired t-test
b. two sample (independent) t-test
(2) The alternative hypothesis is:
Answer: ___________ (Check all that apply) (Please answer with letter a-g only; Please arrange your answer in
alphabetic order with no comma or space in between, for example, ab, bc, abc or abcd)
a. The mean different in height from the 2pm and 5 pm student populations is equal to zero.
b. The mean different in height from the 2pm and 5 pm student populations is NOT zero.
c. The mean different in height from the 2pm and 5 pm student populations larger than zero.
d. Population mean difference in height between the 2pm and 5pm classes µ5pm - µ2pm = 0
e. Population mean difference in height between the 2pm and 5pm classes µ5pm - µ2pm ≠ 0
f. Population mean difference in height between the 2pm and 5pm classes µ5pm - µ2pm > 0
g. Population mean difference in height between the 2pm and 5pm classes µ5pm - µ2pm < 0
(3) Sample size N for the 2pm student population = ___________ (answer whole number only)
Sample size N for the 5pm student population = ___________ (answer whole number only)
(4) Degree of freedom = ___________ (answer whole number only)
(5) calculated t value = ___________ (Please report your answer to 3 decimal places.)

Answer 1

## Q ) In fall 2010, students in my 2 p.m. section of the Introduction to Biological Science I class reported their height
below on the first column of the table, while my 5 p.m. section reported their height on the second column. I
wondered: are the average heights of these two sections significantly different?

## (1)  Based on the nature of the data, you identify and determine that _____ t-test is the most appropriate test to
evaluate the difference in height between the 2pm and 5pm student populations.
Answer: a. paired t-test

## 2) The alternative hypothesis is:
Answer: be

(Check all that apply) (Please answer with letter a-g only; Please arrange your answer in
alphabetic order with no comma or space in between, for example, ab, bc, abc or abcd)

b. The mean different in height from the 2pm and 5 pm student populations is NOT zero.

e. Population mean difference in height between the 2pm and 5pm classes µ5pm - µ2pm ≠ 0

## (3) Sample size N for the 2pm student population = 18

  Sample size N for the 5pm student population = 18

## (4) Degree of freedom = 17 ( N-1)

## (5) calculated t value = 1.678  (Please report your answer to 3 decimal places.)

### below steps not include in the question : i calculate for find out the result is significant or not use standard alpha = 5 %

## critical value : 2.1098 ( used T.DIST(1.678 , 17 , 2)

## Decision : we reject Ho if test statistics value is > critical value here test statistics value is less than critical value we fail to reject Ho .

## Conclusion : There is not or insufficient evidence to conclude that

Population mean difference in height between the 2pm and 5pm classes µ5pm - µ2pm ≠ 0

### Excel output : we can use Excel tool and solve :  

first calculated t value without function and for checking used tools :