Question

NOTE: The numerical values in this problem have been modified for testing purposes.

According to the Centers for Disease Control and Prevention, obesity rates among children have increased dramatically over the past three decades, from a low of about 5% to 18% as of 2010. A study examined the effect of family-based food-counseling sessions provided by trained professionals. The study randomly assigned obese children aged 9 to 12 years to either the counseling intervention or a control group not receiving any food counseling. The children’s weight changes (in pounds, lb) after 15 weeks for both conditions are displayed in the tables below:

Intervention

-16.5	-14.8	-11.8	-9.6	-9.5	-9.1	-8.2	-7.3	-6.5	-5.7
-5.6	-5.6	-5.5	-5.5	-5.1	-5	-5	-4.8	-4.4	-4.4
-4.1	-4	-4	-3.6	-3.5	-3.1	-3	-2	-1.8	-1.8
-1.4	-1.2	-0.2	-0.1	0	0.2	0.6	1	1.2	1.2
1.4	1.8	2	2.2	2.5	2.8	3.1	4	5.4	5.8
6	6.6	8.2

Control

11.8	10.1	9	8.5	7.1	6.7	6.1	4.8	4.6	4.5
2.8	2.8	2.8	2.7	1.8	1.6	1.2	0.7	0.4	0.1
0.1	-5.1	-5.1

Compute the sample means and standard deviations:

Intervention Group Mean =....... (+0.001) and SD =........ (+0.001)

Control Group Mean =........... (+0.001) and SD =........... (+0.001)

Compute the standard error of the mean =......... (+0.001)

Compute the t-statistic: =......... (+0.001)

This t-statistic has df =............ (+0.1) (Use Software)

The p-value of this t-statistic is = ............(Use Software)

(b) Is there strong evidence that obese children receiving food counseling gain less weight over a 15-week period?

We test:

uI < uC

uI > uC

uI ≠ uC

Conclusion:

No, there is no strong evidence that the weight gain was less in the intervention group.

Yes, there is strong evidence the weight gain was less in the intervention group.

Answer 1

data

result

t-Test: Two-Sample Assuming Equal Variances
	Intervention	control
Mean	-2.409433962	3.47826087
Variance	27.27894775	18.36086957
Observations	53	23
Pooled Variance	24.62762721
Hypothesized Mean Difference	0
df	74
t Stat	-4.751481722
P(T<=t) one-tail	4.83802E-06
t Critical one-tail	1.665706893
P(T<=t) two-tail	9.67603E-06
t Critical two-tail	1.992543495

	Intervention	control
Mean	-2.40943396	3.478261
sd	5.22292521	4.284959
standard error	1.239128166
t	-4.75148172
p-value	4.83802E-06

hypothesis

We test:

uI < uC

p-value for one-tailed test = 4.838*10^(-6) << 0.05

hence we reject the null hypothesis

conclusion

Yes, there is strong evidence the weight gain was less in the intervention group.