Please help me find the value of x!
1 answer:
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Answer:
Option B) Fail to reject the null hypothesis that the true population mean annual salary of full-time college professors in the region is equal to $127,000.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = $127,000
Sample mean, = $126,092
Sample size, n = 160
Alpha, α = 0.10
Sample standard deviation, σ = $8,509
First, we design the null and the alternate hypothesis
We use Two-tailed t test to perform this hypothesis.
Formula:
Now,
Since,
The calculated t-statistic lies in the acceptance region, we fail to reject and accept the null hypothesis.
Option B) Fail to reject the null hypothesis that the true population mean annual salary of full-time college professors in the region is equal to $127,000.
9514 1404 393
Answer:
7.2
Step-by-step explanation:
The problem statement tells you to use the distance formula to find the distance between points A and B. In order to do that, you need to read their coordinates from the graph. You find A(-5, 5) and B(1, 1).
The distance formula is ...
Using the point coordinates, the formula tells us the distance is ...
d = √((1-(-5))² +(1-5)²) = √(6² +(-4)²)
d = √(36 +16) = √52 ≈ 7.2111
Rounding the distance to the nearest tenth, we have ...
length AB ≈ 7.2 units
_____
<em>About the Pythagorean theorem</em>
If you draw point C(-5, 1) on the graph, then you can see that triangle ABC is a right triangle. It has legs AC and BC. You can subtract coordinates or count grid squares to see that the lengths of those legs are AC = 4, BC = 6.
The Pythagorean theorem tells you the square of the hypotenuse (AB) is the sum of the squares of the sides (AC and BC).
AB² = 4² +6² = 16 +36 = 52
AB = √52 . . . . as above