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# Midterm - Assignment Example

Summary
The results (as in table 1) indicate significant differences between the participants age (M = 24.51, SD = 2.09) and the population mean of 25; t(186) = -3.18, p = .00. This implies that most of the participants of the present study had a lower age as compared to the average of…

## Extract of sample "Midterm"

Statistics Question Given the following data; Liberal arts; xbar1 = 16.20, s1 = 2.30, n1 = 236 and Other; xbar2= 13.70, s2 = 9.00, n2 = 321
Step 1: The assumptions of normality of the populations from which the samples are derived are assumed to hold. Moreover, the samples are independent and standard deviations are known.
Step 2: We wish to test the hypotheses that;
H0: There is no statistically significant difference in mean between students majoring in Liberal Arts and other students on the average number of books read per year.
H1: There is a statistically significant difference.
Alternatively, this can be stated as;
H0: μ1 – μ2 = 0, where μ1=mean for Liberal Arts and μ2=mean for others.
H1: μ1 ≠ μ2
Step 3: We set α = 0.05
Step 4: Degrees of freedom are obtained as follows;
df1 (for Liberal Arts) = n1 – 1 = 236 – 1 = 235
df2 (for Others) = n2 – 1 = 321 – 1 = 320
dftotal = (n1 + n2 – 2) or (df1 + df2) = (235 + 320) = 555
Step 5: Since this is a 2-sided test, the critical region is given by t.025, 555= tcritical = 1.96
Step 6: Therefore, we compute the test statistic, t, as follows;
(Montgomery & Runger 2002, p. 339)
Where;
(xbar1 – xbar2) = Observed difference between sample means.
(μ1 – μ2) = Expected difference between population means if H0 is true.
 = Estimate of the standard error of the difference between two sample means.
Where the pooled estimate of variance is given as;

Step 7: Therefore, t = 4.17 > tcritical = 1.96
Step 8: Decision: The null hypothesis (H0) is rejected.
Question 2
The results (as in table 1) indicate significant differences between the participants age (M = 24.51, SD = 2.09) and the population mean of 25; t(186) = -3.18, p = .00. This implies that most of the participants of the present study had a lower age as compared to the average of the population age.
Table 1
Results for mean differences between the sample mean age and population mean age
N
Mean
SD
t
df
Sig.
95% CI
Participant’s Age
187
24.51
2.09
-3.18
186
.00*
[-.79, -.18]
Note. CI = confidence interval
*p < .05
Question 3
Methods
Participants
Before conducting the study, informed consent was first sought from the potential participants who mainly included members of the public. The study recruited a total of 187 participants of whom 76 were assigned the vignettes about a 13-year old and 111 were assigned the vignettes about a 16-year old.
Materials
The materials utilized in the present study included two vignettes, which described a crime. These vignettes were used to collect data from the participants.
Design
The present study involved a between-subjects design. This was pertinent in determining whether the participants who read a vignette about a 13 year old were as more likely to sentence a defendant to LWOP as those who read a vignette about a 16 year old. In this context, the dependent variable was life without parole “LWOP” while the independent variable was the defendant’s age.
Procedure
There were two main variables to be examined in the present study; LWOP and defendant’s age. The vignettes were randomly assigned to the participants. The participants recorded their responses for variable LWOP on a 5 point Likert-type scale (1 = very unlikely, 5 = very likely). On the other hand, the variable defendant’s age had two categories; 13-year old defendants and 16-year old defendants.
Results
Analysis
In order to compare the two groups, independent samples t-tests were conducted on the data obtained.
Findings
The results (as in table 2) indicated lack of significant differences between participants who read a vignette about a 13-year old (M = 1.89, SD = 1.21) and participants who read a vignette about a 16-year old (M = 2.14, SD = 1.34); t(185) = 1.30, p = .19. This implies that the participants who read a vignette about a 13-year old were as likely to sentence the defendant to LWOP as those who read a vignette about a 16-year old.
Table 2
Results for independent samples T-Tests
N
Mean
SD
t
df
Sig.
95% CI
Likelihood of sentencing to LWOP
111
2.14
1.34
1.30
185
.19
[-.13, .63]
Note. CI = confidence interval
References
Montgomery, D.C. & Runger, G.C. (2002). Applied Statistics and probability for engineers. 3rd ed. New York: John Wiley & Sons. Read More
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