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.

	n	sample mean	sample variance
Control Group	70	11.8	21.6
RAP	70	9.0	13.0
Headache	70	12.4	8.5

(a) Compute the sample standard deviations for each group.

The sample standard deviation for the control group is ___ (Round to one decimal place)

The sample standard deviation for children suffering from recurrent abdominal pain? (RAP) is ___ (Round to one decimal place)

The sample standard deviation for children suffering from recurring headaches is ___ (Round to one decimal place)

_________________________________________________________________________________________________________________________

(b)

What sampling method was used for each treatment? group? Why?

A.

Simple random? sampling, because the researchers wanted to be sure that the distributions of the sample means were approcimately normal

B.

Systematic? sampling, because it decreases the sample variabilities

C.

Stratified? sampling, because the researchers wanted to be sure that both children and adolescents were represented in the samples

D.

Cluster? sampling, because it eliminates bias from the researcher and subjects

_________________________________________________________________________________________________________________________

(c)

Use a two sample? t-test for independent samples to determine if there is a significant difference in mean behavior scores between the control group and the RAP group? (assume that both samples are simple random? samples). Use

alpha?equals=0.05.

What are the null and alternative hypotheses being? tested?

A.

Upper H 0 : mu Subscript Upper C Baseline equals mu Subscript Upper RH0: ?C=?R

and Upper H 1 : mu Subscript Upper C Baseline not equals mu Subscript Upper RH1: ?C??R

B.

Upper H 0 : mu Subscript Upper C Baseline greater than or equals mu Subscript Upper RH0: ?C??R

and Upper H 1 : mu Subscript Upper C Baseline less than mu Subscript Upper RH1: ?C<?R

C.

Upper H 0 : mu Subscript Upper C Baseline not equals mu Subscript Upper RH0: ?C??R

and Upper H 1 : mu Subscript Upper C Baseline equals mu Subscript Upper RH1: ?C=?R

What is the? P-value? ___ (Round to three decimal places)

State the appropriate conclusion.

A.

There is not enough evidence to indicate that the mean behavior scores are different for the two groups.

B.

There is enough evidence to indicate that the mean behavior scores are different for the two groups.

_________________________________________________________________________________________________________________________

(d)

Is it necessary to check the normality assumption to answer part? (c)?

A.

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

B.

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

C.

?No, because the significance level being used is alpha?equals=0.05. If alpha ? were? larger, then it would be necessary to check the normality assumption in part? (c).

D.

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

_________________________________________________________________________________________________________________________

?(e) Use the? one-way ANOVA procedure with

alpha?equals=0.05

to determine if the mean behaviour scores are different for the three treatment groups.

What are the null and alternative hypotheses being? tested?

A.

Upper H 0 : mu Subscript Upper C Baseline less than mu Subscript Upper R Baseline less than mu Subscript Upper HH0: ?C<?R<?H

and Upper H 1 : mu Subscript Upper C Baseline greater than or equals mu Subscript Upper R Baseline greater than or equals mu Subscript Upper HH1: ?C??R??H

B.

Upper H 0 : mu Subscript Upper C Baseline equals mu Subscript Upper R Baseline equals mu Subscript Upper HH0: ?C=?R=?H

and

Upper H 1H1?:

at least one of the means is different

C.

Upper H 0 : mu Subscript Upper C Baseline not equals mu Subscript Upper R Baseline not equals mu Subscript Upper HH0: ?C??R??H

and Upper H 1 : mu Subscript Upper C Baseline equals mu Subscript Upper R Baseline equals mu Subscript Upper HH1: ?C=?R=?H

What is the? F-statistic? ___ (Round to three decimal places)

What is the? P-value? ___ (Round to three decimal places)

State the appropriate conclusion.

A.

There is not enough evidence to indicate that at least one of the mean behavior scores is different.

B.

There is enough evidence to indicate that at least one of the mean behavior scores is different.

_________________________________________________________________________________________________________________________

(f) Based on your results from parts? (c) and? (e), 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.

?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.

C.

?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.

Answer 1