In: Math
Scenario: Imagine you are a researcher who is interested in
studying whether sleep deprivation leads to increased reaction
times (i.e., being slower) when driving. You randomly select a
sample of 30 licensed drivers. Fifteen participants are randomly
assigned to get 5 hours of sleep for three consecutive nights. The
other 15 participants are randomly assigned to get 8 hours of sleep
for three consecutive nights. For the purposes of this Assignment,
assume that all participants sleep exactly the required amounts.
After the third night, all participants take a driving simulation
test that measures their reaction times.
Use SPSS to determine if amount of sleep is related to reaction time.
1. Explain whether the researcher should use an
independent-samples t-test or a related-samples t-test for this
scenario. Provide a rationale for your decision.
2. Identify the independent variable and dependent variable.
3. Knowing the researcher believes that people who sleep less will
have slower reaction times, state the null hypothesis and alternate
hypothesis in words (not formulas).
4. Explain whether the researcher should use a one-tailed test or
two-tailed test and why.
5. Identify the obtained t value for this data set using SPSS and
report it in your answer document.
6. State the degrees of freedom and explain how you calculated it
by hand.
7. Identify the p value using SPSS and report it in your answer
document.
8. Explain whether the researcher should retain or reject the null
hypothesis. Provide a rationale for your decision. Are the results
statistically significant?
9. Explain what the researcher can conclude about the relationship
between amount of sleep and reaction times.
Data:
Reaction times in seconds for participants with 5 hours of
sleep
0.22
0.25
0.27
0.25
0.24
0.28
0.24
0.3
0.25
0.21
0.28
0.23
0.29
0.25
0.29
Reaction times in seconds for participants with 8 hours of
sleep
0.21
0.23
0.2
0.24
0.28
0.23
0.3
0.29
0.23
0.21
0.21
0.27
0.29
0.23
0.25
Scenario: Imagine you are a researcher who is interested in studying whether sleep deprivation leads to increased reaction times (i.e., being slower) when driving. You randomly select a sample of 30 licensed drivers. Fifteen participants are randomly assigned to get 5 hours of sleep for three consecutive nights. The other 15 participants are randomly assigned to get 8 hours of sleep for three consecutive nights. For the purposes of this Assignment, assume that all participants sleep exactly the required amounts. After the third night, all participants take a driving simulation test that measures their reaction times.
Use SPSS to determine if amount of sleep is related to reaction time.
1.Explain whether the researcher should use an
independent-samples t-test or a related-samples t-test for this
scenario. Provide a rationale for your decision.
since 30 participants divided in to 2 different groups, independent-samples t-test to be used.
2. Identify the independent variable and dependent
variable.
independent variable : sleep hours
dependent variable: Reaction time
3. Knowing the researcher believes that people who sleep less
will have slower reaction times, state the null hypothesis and
alternate hypothesis in words (not formulas).
Ho: people who sleep 5 hours and people who sleep 8 hours have the same Reaction time.
H1: people who sleep 5 hours have the less Reaction time than people who sleep 8 hours
4. Explain whether the researcher should use a one-tailed test
or two-tailed test and why.
We should use a one-tailed test because alternate hypothesis have < sign.
5. Identify the obtained t value for this data set using SPSS
and report it in your answer document.
obtained t value= 1.080
6. State the degrees of freedom and explain how you calculated
it by hand.
degrees of freedom = n1+n2-2 =15+15-2=28
7. Identify the p value using SPSS and report it in your answer
document.
P value from spss output=0.289.
8. Explain whether the researcher should retain or reject the
null hypothesis. Provide a rationale for your decision. Are the
results statistically significant?
Spss output p value is two sided. But out test is one sided. Therefore our required p value
= 0.289/2 = 0.1445
Since the p value 0.1445 > 0.05 level of significance, Ho is not rejected.
Results are not statistically significant.
9. Explain what the researcher can conclude about the relationship between amount of sleep and reaction times.
The researcher can conclude that there is no relationship between amount of sleep and reaction times.
SPSS OUTPUT
Group Statistics |
|||||
sleep hours |
N |
Mean |
Std. Deviation |
Std. Error Mean |
|
Reaction time |
5.00 |
15 |
.2567 |
.02717 |
.00701 |
8.00 |
15 |
.2447 |
.03335 |
.00861 |
Independent Samples Test |
||||||||||
Levene's Test for Equality of Variances |
t-test for Equality of Means |
|||||||||
F |
Sig. |
t |
df |
Sig. (2-tailed) |
Mean Difference |
Std. Error Difference |
95% Confidence Interval of the Difference |
|||
Lower |
Upper |
|||||||||
Reaction time |
Equal variances assumed |
1.060 |
.312 |
1.080 |
28 |
.289 |
.01200 |
.01111 |
-.01075 |
.03475 |
Equal variances not assumed |
1.080 |
26.900 |
.290 |
.01200 |
.01111 |
-.01079 |
.03479 |