The 90% confidence interval for the population mean is 78.1905<x<81.8095
<h3>Confidence interval</h3>
The formula for calculating the confidence interval is expressed as:
CI = x ± z*s/√n
Given the following parameters
mean "x" = 80
z = 1.645
s = 5.5
n = 25
Substitute
CI = 80 ± 1.645*5.5/√25
CI = 80 ± 1.8095
CI = {78.1905, 81.8095}
Hence the 90% confidence interval for the population mean is 78.1905<x<81.8095
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Answer:
a. proportions have not changed significantly
Step-by-step explanation:
Given
Business College= 35 %
Arts College= 35 %
Education College = 30%
Calculated
Business College = 90/300= 9/30= 0.3 or 30%
Arts College= 120/300= 12/30= 2/5= 0.4 or 40%
Education College= 90/300= 9/30 = 0.3 or 30%
First we find the mean and variance of the three colleges using the formulas :
Mean = np
Standard Deviation= s= 
Business College
Mean = np =300*0.3= 90
Standard Deviation= s=
=
= 7.94
Arts College
Mean = np =300*0.4= 120
Standard Deviation= s=
=
= 8.49
Education College
Mean = np =300*0.3= 90
Standard Deviation= s=
=
= 7.94
Now calculating the previous means with the same number of students
Business College
Mean = np =300*0.35= 105
Arts College
Mean = np =300*0.35= 105
Education College:
Mean = np =300*0.3= 90
Now formulate the null and alternative hypothesis
Business College
90≤ Mean≥105
Arts College
105 ≤ Mean≥ 120
Education College
U0 : mean= 90 U1: mean ≠ 90
From these we conclude that the proportions have not changed significantly meaning that it falls outside the critical region.
Answer:
276 miles, $ 20.148
Step-by-step explanation:
Given:
Donald Duck's car travels in 1 gallon gas = 30 miles
Cost of 1 gallon = $ 2.19
Question asked:
Distance travel in 9.2 gallons = ?
Cost of 9.2 gallons of gas = ?
Solution:
By applying unitary method:
His car travels in 1 gallon = 30 miles
His car will travel in 9.2 gallons =
= 276 miles
Cost of 1 gallon = $ 2.19
Cost of 9.2 gallons =
= $ 20.148
Answer: D) 154 degrees clockwise about point A
========================================================
Explanation:
We have n = 7 sides here, so this is a heptagon.
Assuming this is a regular heptagon, then we can say that 360/n = 360/7 = 51.4285714285714 is the angle in which we can rotate the figure to have it map onto itself.
What does that mean? It means that if we were to apply this rotation, then the "before" and "after" (aka preimage and image) will be identical.
The angle value 51.4285714285714 rounds to 51, and unfortunately none of the answer choices come closer to this.
But we can scale things up. Instead of doing 1 rotation, we can do 3 rotations of 51.4285714285714 degrees each to get 3*51.4285714285714 = 154.285714285714
The value then rounds to 154 degrees. This can happen clockwise or counterclockwise.