Question

2) A company making mattresses wants to test two different designs on elderly people who typically have more trouble sleeping through the night, to see which is more effective at keeping people asleep for more hours. One is a mattress that conforms to the body (mattress #1) the other is a mattress that elevates to different levels to help with sleep apnea and snoring (mattress #2). The company wants to know which mattress makes more of a difference in helping elderly people sleep, mattress 1 or 2. Two groups of elderly people (10 in each) are asked to sleep in cach mattress for 2 weeks and how many hours they slept altogether is recorded. Is one mattress significantly more helpful than the other? Mattress 1 Sleep Mattress 2 Hours of Sleep 7 12 9.5 10 10 14 13 lulul 2 10 17 19 12 18 15 1 8 7 What is the independent variable? b. What is the dependent variable? c. What test did you use to analyze the data? I d. Is the test significant? How do you know? e. Write the statistical notation in APA style Focus

Answer 1

2.
Given that,
mean(x)=14
standard deviation , s.d1=3.1972
number(n1)=10
y(mean)=6.05
standard deviation, s.d2 =2.9293
number(n2)=10
null, Ho: u1 = u2
alternate, H1: u1 > u2
level of significance, α = 0.05
from standard normal table,right tailed t α/2 =1.833
since our test is right-tailed
reject Ho, if to > 1.833
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =14-6.05/sqrt((10.22209/10)+(8.5808/10))
to =5.798
| to | =5.798
critical value
the value of |t α| with min (n1-1, n2-1) i.e 9 d.f is 1.833
we got |to| = 5.79769 & | t α | = 1.833
make decision
hence value of | to | > | t α| and here we reject Ho
p-value:right tail - Ha : ( p > 5.7977 ) = 0.00013
hence value of p0.05 > 0.00013,here we reject Ho
ANSWERS
---------------
a.
The independent variable is the amount of chores you do because this is the variable you have control over.
b.
A dependent variable represents a quantity whose value depends on how the independent variable is manipulated.
c.
null, Ho: u1 = u2
alternate, H1: u1 > u2
test statistic: 5.798
critical value: 1.833
d.
decision: reject Ho
p-value: 0.00013
e.
we have enough evidence to support the claim that mean of mattress 2 is more helpful than other.
3.
Given that,
mean(x)=39
standard deviation , s.d1=25.7164
number(n1)=10
y(mean)=285.2
standard deviation, s.d2 =31.0977
number(n2)=10
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.262
since our test is two-tailed
reject Ho, if to < -2.262 OR if to > 2.262
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =39-285.2/sqrt((661.33323/10)+(967.06695/10))
to =-19.293
| to | =19.293
critical value
the value of |t α| with min (n1-1, n2-1) i.e 9 d.f is 2.262
we got |to| = 19.29334 & | t α | = 2.262
make decision
hence value of | to | > | t α| and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -19.2933 ) = 0
hence value of p0.05 > 0,here we reject Ho
ANSWERS
---------------
a.
The independent variable is the amount of chores you do because this is the variable you have control over.
b.
A dependent variable represents a quantity whose value depends on how the independent variable is manipulated.
c.
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: -19.293
critical value: -2.262 , 2.262
d.
decision: reject Ho
p-value: 0
e.
we have enough evidence to support the claim that difference of means between hours of study and GRE score.

4.
a.
Statistical methods involved in carrying out a study include planning, designing, collecting data, analysing, drawing meaningful interpretation and reporting of the research findings.
The statistical analysis gives meaning to the meaningless numbers, thereby breathing life into a lifeless data.
b.
The independent variable is the amount of chores you do because this is the variable you have control over.
c.
A dependent variable represents a quantity whose value depends on how the independent variable is manipulated.
d.
T test for difference of means we use