Question

This data set presents 17 paired data corresponding to the weights of girls before and after treatment for anorexia.

Prior	Post
83.8	95.2
83.3	94.3
86.0	91.5
82.5	91.9
86.7	100.3
79.6	76.7
76.9	76.8
94.2	101.6
73.4	94.9
80.5	75.2
81.6	77.8
82.1	95.5
77.6	90.7
83.5	92.5
89.9	93.8
86.0	91.7
87.3	98.0

a. What is the appropriate t-test?

b. What are the dependent and independent variables?

c. State the null and alternative hypothesis.

d. For α =.05, two tailed, what is the degrees of freedom and t_crit?

df =

t_crit =)

d. What is t_obs? (Show the calculation. Show SS calculation)

e. Calculate 95% confidence interval of the mean difference (Show the calculation.)

f. Write your conclusion as it would appear in a research paper. Report t-statistic (don’t forget to put the df), p-value, and the 95% confidence interval that support your decision.

Answer 1

(a)

Dependent Samples (paired) t test

(b)

Dependent Variable: weights of girls

Independent Variable: treatment for anorexia.

(c)

H0: Null Hypothesis: 0 (there is no significant change in weight between before and after treatment for anorexia. )

HA: Alternative Hypothesis: 0 (there is significant change in weight between before and after treatment for anorexia ) (Claim)

the degrees of freedom = df = 17 - 1 = 16

=0.05

From Table, critical values of t_crit = 2.12

(d)

From the given data, values of d = Prior - Post are got as follows:

d = Prior - Post = - 11.4, - 11.0, - 5.5, - 9.4, - 13.6, 2.9, 0.1, - 7.4, -21.5, 5.3, 3.8, - 13.4, - 13.1, - 9.0, - 3.9, - 5.7, - 10.7

From d values,the following Table is calculated:

n = 17

= - 123.5/17 = - 7.265

d	d -	(d - )2
-11.4	-4.1353	17.1007
-11.0	-3.7353	13.9524
-5.5	1.7647	3.1142
-9.4	-2.1353	4.5595
-13.6	-6.3353	40.1360
2.9	10.1647	103.3212
0.1	7.3647	54.2389
-7.4	-0.1353	0.0183
-21.5	-14.2353	202.6436
5.3	12.5647	157.8718
3.8	11.0647	122.4277
-13.4	-6.1353	37.6418
-131	-5.8353	34.0507
-9.0	-1.7353	3.0112
-3.9	3.3647	11.3212
-5.7	1.5647	2.4483
-10.7	-3.4353	11.8012
Total =		819.6588

Standard deviation = s_d = 7.157

SE = s_d/

= 7.157/

= 1.7358

Test Statistic is given by:

So,

t_obs = - 4.185

By Technology, p - value = 0.0007

Since calculated value of t = - 4.185 is less than critical value of t = - 2.12, the difference is significant. Reject null hypothesis.

Conclusion:
The data support the claim that there is significant change in weight between before and after treatment for anorexia.

(e)

Confidence Interval:

= -7.265 (2.12 X 1.7358)

= - 7.265 3.6799

= ( - 10.9448 , - 3.5851)

So,

Answer is:

( - 10.9448 , - 3.5851)

(f)

The research question in this study is: Is there any significant change in weight between before and after treatment for anorexia?

A set of 17 dependent samples containing data on the weights of girls before and after treatment for anorexia. The mean difference obtained was = - 7.265 with Standard deviation = s_d = 7.157.

Two Tail Dependent Samples t test was done with Significance level = = 0.05 and degrees of freedom = 16. The reported t value was t_obs = - 4.185. p - value was 0.0007. Since calculated value of t = - 4.185 is less than critical value of t = - 2.12, the difference is significant. Reject null hypothesis Conclusion was: The data support the claim that there is significant change in weight between before and after treatment for anorexia. The 95% confidence interval for the difference before and after treatment for anorexia.was got as ( - 10.9448 , - 3.5851). Since all values in the confidence interval are negative, it supports our conclusion that there is significant change in weight between before and after treatment for anorexia.