Question

A professor of women's studies is interested in determining if stress affects the menstrual cycle. Ten women are randomly sampled for an experiment and randomly divided into two groups. One of the groups is subjected to high stress for two months while the other lives in a relatively stress-free environment. The professor measures the menstrual cycle (in days) of each woman during the second month. The following data are obtained.

High stress 20 23 18 19 22
Relatively stress free 26 31 25 26 30
1. The obtained value of the appropriate statistic is ____.
A. tobt = -4.73.
B. tobt = -4.71.
C. tobt = -3.05.
D. tobt = -.047.
2. The df for determining tcrit are ____.
A. 4.
B. 9.
C. 8.
D. 3.
3. Using a = .052 tail, tcrit = ____.
A. +- 2.162.
B. +- 2.506.
C. +- 2.462.
D. +- 2.306.
4. Using a = .052 tail, your conclusion is ____.
A. Accept H0; stress does not affect the menstrual cycle.
B. Retain H0; we cannot conclude that stress affects the menstrual cycle.
C. Retain H0; Stress affects the menstrual cycle.
D. Reject H0; stress affects the menstrual cycle.

Answer 1

-4.73

8

±2.306

D. Reject H0; stress affects the menstrual cycle.

Explanation:

Samples:

High stress 20 23 18 19 22

Relatively stress free 26 31 25 26 30

Using calculator :

Mean, x1 = 20.4 ; n = 5 ;

Standard deviation, s1 = 2.07

Mean, x2 = 27. 6; n = 5 ;

Standard deviation, s2 = 2.70

The test statistic :

(x1 - x2) / sqrt[(s1²/n1 + s2²/n2)]

(20.4 - 27.6) /sqrt[(2.07²/5 + 2.7²/5)]

-7.2 / 1.523 = - 4.73

Df = n1 + n2 - 2

df = 5 + 5 - 2 = 8

From t-value distribution :

df = 8 ; α = 0.052

Tcritical = +- 2.306

|Tstatistic | > | Tcritical | ; Reject H0