A college student is interested in testing whether business majors or liberal arts majors are better at trivia. The student give
1 answer:
Answer:
There is no notable difference between the two averages at a 5% significance level.
Step-by-step explanation:
A college student wanted to investigate whether business majors or liberal arts majors performed better in trivia.
The student administered a trivia quiz to 30 business majors, achieving an average score of 86. The same quiz was given to 30 liberal arts majors, with an average score of 89.
This process involved hypothesis testing to compare the means of two different disciplines. n =30
Since no specific claim is made regarding which group is better, a two-tailed test is appropriate.
The p-value achieved exceeds our alpha level,
indicating no significant difference exists between the average scores of the two groups, so we accept the null hypothesis.
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Y = 3bx - 7x
y = x(3b - 7)
Assuming 3b - 7 ≠ 0, divide both sides by 3b - 7.
Solution:
y = x(3b - 7)
Assuming 3b - 7 ≠ 0, divide both sides by 3b - 7.
Solution:
Response:
a. As student debt rises, current investment diminishes.
b. Y= 68778.2406 - 1.9112X
For each dollar increase in college debt, the average current investments decrease by 1.9112 dollars.
c. A substantial linear correlation exists between college debt and current investment as the P-value falls below 0.1.
d. Y= $59222.2406
e. R²= 0.9818
Step-by-step breakdown:
Hello!
Data has been gathered on a random sample of 20 individuals who completed their college education five years ago. The variables under consideration are:
Y: Current investment by an individual who graduated from college five years prior.
X: Total debt of an individual upon graduating five years ago.
a)
To explore the relationship between debt and investment, creating a scatterplot with the sample data is ideal.
The scatterplot demonstrates a negative correlation, indicating that as these individuals' debt increases, their current investments decrease.
Therefore, the statement that accurately describes this is: As college debt rises, current investment decreases.
b)
The population regression equation is Y= α + βX +Ei
To develop this equation, estimates for alpha and beta are required:
a= Y[bar] -bX[bar]
a= 44248.55 - (-1.91)*12829.70
a= 68778.2406
b=
b=
b= -1.9112
∑X= 256594
∑X²= 4515520748
∑Y= 884971
∑Y²= 43710429303
∑XY= 9014653088
n= 20
Averages:
Y[bar]= ∑Y/n= 884971/20= 44248.55
X[bar]= ∑X/n= 256594/20= 12829.70
The estimated regression equation becomes:
Y= 68778.2406 - 1.9112X
For every dollar increase in college debt, the average current investments drop by 1.9112 dollars.
c)
To evaluate if there's a linear regression between these variables, the following null hypotheses are formulated:
H₀: β = 0
H₁: β ≠ 0
α: 0.01
Testing can be performed utilizing either a Student t-test or Snedecor's F (ANOVA)
Using t= b - β = -1.91 - 0 = -31.83
Sb 0.06
The critical area and P-value for this test is two-tailed. The P-value equals: 0.0001
Since this P-value is underneath the significance level, we reject the null hypothesis.
In the case of ANOVA, the rejection area is also one-tailed to the right, corresponding to the P-value.
The P-value remains: 0.0001
Using this method, we similarly reject the null hypothesis.
This indicates that 98.18% of the variability in current investments relates to college graduation debt within the projected regression model: Y= 68778.2406 - 1.9112X
I trust this is beneficial!
