What does it mean “2 times the difference between 49.5 and 37.5?
1 answer:
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Answer:
The decision rule for rejecting the null hypothesis is
Step-by-step explanation:
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 410 gram setting. It is believed that the machine is underfilling the bags.
At the null hypothesis, we test if the mean weight of the bag is the desired value of 410, that is:
At the alternate hypothesis, we test if the bag is underfilled, that is, the mean weight is below the desired value, so:
Type of test:
As we test if the mean is less than a value, we have a left-tailed test.
We have the standard deviation for the sample, which means that the t-distribution is used.
We have 22 - 1 = 21 degrees of freedom, with a level of significance of 0.05.
Using a calculator, the critical value is
Determine the decision rule for rejecting the null hypothesis.
We reject the null hypothesis if the test statistic is less than the critical value, so the decision rule for rejecting the null hypothesis is
<h3>Answer: Choice B</h3>
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Explanation:
Let's look at choice A
The left hand side simplifies as follows
This means the equation is the same as
. Notice how the left and right sides are identical expressions. They both involve 3x and a 1. This means this equation has infinitely many solutions. We can rule out choice A.
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I'll skip choice B and come back
Let's move onto choice C.
The given equation transforms into
through similar steps as choice A shows.
If we were to subtract 5x from both sides, all of the x terms go away on both sides. We'd be left with the equation which is always false, which means that the original equation is always false.
Therefore, the equation of choice C has no solutions. We consider this equation inconsistent. We rule out choice C because of all this.
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Choice D is pretty much the same as choice A even down to the conclusion of getting infinitely many solutions. The left hand side simplifies fully into the right hand side. The two sides are identical; hence, we have an identity. An identity is true for all allowed x values in the domain.
In other words, whatever x value you pick it will make the equation true. So we can rule this out because we want one solution only.
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Only choice B is left. You'll notice that after simplifying the left hand side, the x term on the left side doesn't turn into 2x. So there's no way to get the options of "infinitely many solutions" or "no solutions". Those two cases only happen when we have the same x terms on both sides.
Put another way, the two slopes of each side are different which produces nonparallel lines that intersect at exactly one location. This intersection location is the solution. Specifically, the x coordinate of the (x,y) location is the solution.