## Description

Biostatistics homework involving SAS, parameters, statistical significance and p-values.

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Question 1:

(a) Two sample t-tests

Mean number of hours a person with sleep disturbance (i.e. self-reported problems

sleep) sleeps on average each night = ys

Mean number of hours a person without sleep disturbance (i.e. self-reported problems

sleep) sleeps on average each night = ns

Null Hypothesis

H 0 : ys = ns ; Average number of hours a person sleeps either with

or without sleep disturbance.

Alternate Hypothesis

H 0 : ys ns ; Average number of hours a person sleeps with sleep

Disturbance less than a person sleeps without sleep

Disturbance

(b) For two sample independent pooled test, p = 0.0001 .

This test is known as a two sample (or unpaired) t-test. It produces a “p-value”, which

can be used to decide whether there is evidence of a difference between the two

population means. The p-value is the probability that the difference between the

sample means is at least as large as what has been observed, under the assumption

that the population means are equal. The smaller the p-value, the more surprised we

would be by the observed difference in sample means if there really was no

difference between the population means. Therefore, the smaller the p-value, the

stronger the evidence is that the two populations have different means .

(c) Estimate of the pooled standard deviation =1.4111

(d) Estimated mean difference of hours slept between those who report trouble

sleeping compared to those who do not = −0.7578

(e) Standard error of the average difference between two groups = 0.0403

(f) 95% confidence interval for the population mean difference of hours slept between

those who report trouble sleeping compared to those who do not is (−0.8368,−0.6787)

(g) 99% confidence interval for the population mean difference of hours slept between

those who report trouble sleeping compared to those who do not is:

1

1

(x − x )− t

2 1

2 1

(

)

s

+

,

x

−

x

+

t

s

+

p

p

ys

ns

/2

ys ns / 2

n

�...