Compare 36% of 2.5b and 1.5% of 80b
1 answer:
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Answer:
Step-by-step explanation:
Hello!
Given the linear regression of Y: "Annual salary" as a function of X: "Mean score on teaching evaluation" of a population of university professors. It is desired to study whether student evaluations are related to salaries.
The population equation line is
E(Y)= β₀ + β₁X
Using the information of a n= 100 sample, the following data was calculated:
R²= 0.23
Coefficient Standard Error
Intercept 25675.5 11393
x 5321 2119
The estimated equation is
^Y= 25675.5 + 5321X
Now if the interest is to test if the teaching evaluation affects the proffesor's annual salary, the hypotheses are:
H₀: β = 0
H₁: β ≠ 0
There are two statistic you can use to make this test, a Student's t or an ANOVA F.
Since you have information about the estimation of β you can calculate the two tailed t test using the formula:
~
= 25.1109
The p-value is two-tailed, and is the probability of getting a value as extreme as the calculated under the distribution
p-value < 0.00001
I hope it helps!
Answer:
Critical value: T = 1.337
The 80% confidence interval for the mean repair cost for the stereos is between $45.991 and $86.689
Step-by-step explanation:
We have the standard deviation for the sample. So we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 17 - 1 = 16
80% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 16 degrees of freedom(y-axis) and a confidence level of . So we have T = 1.337, which is the critical value
The margin of error is:
M = T*s = 1.337*15.22 = 20.349
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 66.34 - 20.349 = $45.991
The upper end of the interval is the sample mean added to M. So it is 66.34 + 20.349 = $86.689
The 80% confidence interval for the mean repair cost for the stereos is between $45.991 and $86.689