Malaika Wauters Math 11 - Lab 7
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University of California, San Diego *
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Course
11
Subject
Mathematics
Date
May 30, 2024
Type
Pages
7
Uploaded by MegaRose1330
Malaika Wauters
Math 11
Denise Rava
Lab 7: SAT Scores and Cloud Seeding
1.
Examine the distributions of the Math and Verbal SAT scores. Do they appear to be
approximately normally distributed? Are there any outliers? What about the distribution
of the GPAs?
a.
The distributions of the Math and
verbal SAT scores appear to be normally
distributed, as seen in the bell shaped
curve on the histograms to the left,
however, there are outliers in both sets of
data on the lower end. The distribution of
the GPAs is also bell shaped and
approximately normal but there are no
evident outliers that can be assumed from
the histogram.
2.
How does the performance of males compare to the performance of females on the Math
SAT test? What about the Verbal SAT test? How do the first-year GPAs of male and
female students compare?
a. The data collected for the Math test section score show that Males have a slightly
higher median in comparison to females but also a wider spread of data. While both
males and females have two outliers, both male outlier scores are on the lower end while
1 outlier score achieved by females is higher than average.
b. In regards to the Verbal test scores, both male and females have approximately the
same median score but the spread of data for females is greater between the median and
upper quartile while the spread is wider for males below the median. The data only shows
1 outlier for females and 3 for males.
c. The boxplot for the GPAs of males and
females shows that the median GPA
among males is lower than that of
females, although females have a greater
interquartile range. The also are no
outlier GPA scores amongst females
while there are 2 outliers for males on the
higher end.
3.
Based on what you observed from examining the data graphically, does it appear that the
assumptions required to conduct t-tests are met?
a.
Yes, independence is assumed and also the histograms in question1 demonstrate a
normal distribution bell shaped curve, therefore the conditions to perform t-tests
should be adequate.
4.
Do macroeconomics students at Vanderbilt score significantly higher on the Math SAT
than the national average (which in the mid-1980s was around 470)?
a.
One sample t-test & one sided
b.
Null hypothesis H
0
: μ = 470
c.
Alternative hypothesis H
A
: μ >470
d.
Degrees of freedom = n-1 = 391-1 = 390
e.
T statistic = 50.80
f.
P-value: P(t > 50.80) < 0.005
g.
Given that the p-value is less than 0.005, which is less than 0.05 (the test
significance level), we can reject the null hypothesis and there is evidence that the
mean Math SAT score at Vanderbilt was higher than the national average.
5.
Do macroeconomics students at Vanderbilt score significantly higher on the Verbal SAT
than the national average (which in the mid-1980s was around 425)?
a.
One sample t-test & one sided
b.
Null hypothesis H
0
: μ = 425
c.
Alternative hypothesis H
A
: μ >425
d.
Degrees of freedom = n-1 = 391-1 = 390
e.
T statistic = 38.45
f.
P-value: P(t > 38.45) < 0.005
g.
Given that the p-value is less than 0.005, which is less than 0.05 (the test
significance level), we can reject the null hypothesis and claim that there is
sufficient evidence that the mean Verbal SAT score at Vanderbilt was higher than
the national average of 425.
6.
Report a 95 percent confidence interval for the true mean Math SAT score. Do 95 percent
of students have Math SAT scores that fall within this interval? Explain your answer.
a.
One sample t-test & two sided
b.
Null hypothesis H
0
: μ = 624.9
c.
Alternative hypothesis H
A
: μ /= 624.9
d.
95% CI = (619.5,630.2)
e.
The 95% confidence interval means that we can claim that the true mean falls in
this interval with 95% confidence, but it does not mean that 95% of the students
scored in this range for the Math section of the SAT.
7.
Is there a statistically significant difference between the Verbal and Math scores of
microeconomics students at Vanderbilt?
a.
Paired t-test & 2 sided alternative
b.
Null hypothesis H
0
: Math = Verbal
c.
Alternative hypothesis H
A
: Math /= Verbal
d.
T statistic = -20.4
e.
P <0.0001, given that the p value is less than 0.05, we reject the null hypothesis.
8.
Is there a statistically significant difference between the performances of males and
females on the Verbal SAT? Construct a 95 percent confidence interval for the difference.
Does it include zero? Relate this to the conclusion of your test.
a.
2 sample t-test
b.
T statistic = 0.60
c.
Degrees of freedom = n-1 = 124-1 = 123
d.
P-value: P(|t| >0.6) = 2 x P(t >0.6) → 2 x P(t >1.289) = 0.20
e.
Given that the p value is actually greater than 0.20, we cannot reject the null
hypothesis and conclude that there is no significant statistical difference between
male and female verbal SAT scores.
f.
(-9.38, 17.58)
g.
The 95% confidence interval includes 0, since we failed to reject the null
hypothesis and claimed that there is no difference in verbal SAT performance
between males and females, the confidence interval containing 0 confirms that.
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