Question

Researchers wanted to determine if the psychological profile of healthy children was different than for children suffering from recurrent abdominal pain​ (RAP) or recurring headaches. A total of 210 children and adolescents were studied and their psychological profiles were graded according to a child behavior checklist. Children were stratified in two age​ groups: 4 to 11 years and 12 to 18 years. The results of the study are summarized in the accompanying table. Complete parts ​(a) through​ (f) below.

TABLE: n Sample Mean Sample Variance

CONTROL GROUP 70 11.8 21.6

RAP 70 9.1 13.0

HEADACHE 70 12.4 8.5

a.) Is it necessary to check the normality assumption

Upper H 0 : mu Subscript Upper C Baseline not equals mu Subscript Upper RH0: μC≠μR

and Upper H 1 : mu Subscript Upper C Baseline equals mu Subscript Upper R

​No, because they are large​ samples, it can be assumed that the distributions of the sample means are approximately normal.

​Yes, because they are large​ samples, it cannot be assumed that the distributions of the sample means are approximately normal.

​Yes, because the samples are not large enough to assume normality.

​No, because the significance level being used is alphaαequals=0.05

If alphaα were​ larger, then it would be necessary to check the normality assumption

b.) What is the F statistic

c.) What is the p-value

d.) Can you determine if there is a significant difference between the mean scores of the RAP group and the headache group?

A.) No, because the mean scores of the RAP group and the headache group are the same.

​B.) Yes, because both part​ (e) and part​ (c) concluded that there were significant differences between the mean scores of the RAP group and the headache group.

C.) ​No, because the result from part​ (e) only indicates that at least one mean is different and it does not indicate which pairs are different nor even how many. The result from part​ (c) indicates that the mean scores for the control group and the RAP group are​ different, but additional pairs could also be significantly different.

Answer 1

TABLE: n Sample Mean Sample Variance

CONTROL GROUP 70 11.8 21.6

RAP 70 9.1 13.0

HEADACHE 70 12.4 8.5

a.) Is it necessary to check the normality assumption

Ha: μC=μR

Ha: μC≠μR

​No, because they are large​ samples, it can be assumed that the distributions of the sample means are approximately normal.

using excel>addin>phstat>two sample t

we have

Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.05
Population 1 Sample
Sample Size	70
Sample Mean	11.8
Sample Standard Deviation	4.64758
Population 2 Sample
Sample Size	70
Sample Mean	9.1
Sample Standard Deviation	3.605551
Intermediate Calculations
Population 1 Sample Degrees of Freedom	69
Population 2 Sample Degrees of Freedom	69
Total Degrees of Freedom	138
Pooled Variance	17.3
Difference in Sample Means	2.7
t Test Statistic	3.840385
Two-Tail Test
Lower Critical Value	-1.9773
Upper Critical Value	1.977304
p-Value	0.000187
Reject the null hypothesis

b.)the t statistic = 3.840

c.) the p-value =0.0002

d.)

​B.) Yes, because both part​ (e) and part​ (c) concluded that there were significant differences between the mean scores of the RAP group and the headache group.