# Mathematics

Sample problems are as under: (detailed problems are attached herewith in word file)

A researcher conducted a study using a randomly selected group of 40 students, giving them all a standardized performance evaluation (ranging from 0 – 10) to establish a baseline score – then had them all attend a one-week training program – then administered a second standardized performance evaluation to see if the training program had made a significant difference in the students’ average performance.

Data Output for this Assignment is found on the last page.

1.(4 points) State (using symbols and words) the null hypothesis and the alternative hypothesis for the Dependent-Samples t Test.

H0:

Ha:

2.(3 points) Complete the following tables for the Baseline / One-Week Dependent-Samples t-Test (Do not round – use the values from SPSS):

Performance

N

Mean

Standard

Deviation

Standard Error

of the Mean

Baseline

One-Week

t

df

Sig.

(2-tailed)

Paired Mean

Difference

Paired Standard Deviation

95% CI of the Difference

Lower            Upper

A researcher conducted a study to examine the effects of secure, anxious, and avoidant attachment styles on the physiology of sleep. Participants were selected using a stratified random sampling approach to ensure representation of each of the three styles. The sleep patterns of 30 secure, 30 anxious, and 30 avoidant children were monitored. Of primary importance to the researcher was the overall percentage of time each child spent in deep (delta) sleep. Following is the average amount of time that each child spent in delta sleep, expressed as a percentage of total sleep time (ranging from 0.0 to 100.0). For the attachment styles, 1 = secure, 2 = anxious, and 3 = avoidant.

Data Output for this Assignment is found on the last four pages.

1.(2 points) What would the null hypothesis be for this study? Show/write the appropriate symbols and expression in words.

H0:     ???

.

2.(2 points) What would the alternative hypothesis be for this study? Show/write the appropriate symbols and expression in words.

Ha:

3.Prior to examining whether the group means differ; you need to test the underlying assumptions of the one-way analysis of variance.

3.a.(2 points) Has the assumption of independence been met for this data?