Five students divided 74 base-ten rods equally among them. how many base-ten rods were left over?
1 answer:
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Answer:
Step-by-step explanation:
We'll just work on solving both so you can see what's involved in solving an absolute value equation. Because an absolute value is a distance, we can have that distance being both to the right on the number line of the number in question or to the left. For example, from 2 on the number line, the numbers that are 5 units away are 7 and -3. Using that logic, we will simplify the equation down so we can set up the 2 basic equations needed to solve for x.
If then
What you need to remember here is that you cannot distribute into a set of absolute values like you would a set of parenthesis. The -2 needs to be divided away:
Now we can set up the 2 main equations for this which are
.5x + 1.5 = .5 and .5x + 1.5 = -.5
Knowing that an absolute value will never equal a negative number (because absolute values are distances and distances will NEVER be negative), once we remove the absolute value signs we can in fact state that the expression on the left can be equal to a negative number on the right, like in the second equation above.
Solving the first one:
.5x = -1 so
x = -2
Solving the second one:
.5x = -2 so
x = -4
Answer:
a) Reject H₀
b) [0.31; 3.35]
Step-by-step explanation:
Hello!
a) The objective of this example is to compare if the population means of the production rate of the assembly lines A, B and C. To do so the data of the production of each line were recorded and an ANOVA was run using it.
The study variable is:
Y: Production rate of an assembly line.
Assuming that the study variable has a normal distribution for each population, the observations are independent and the population variances are equal, you can apply a parametric ANOVA with the hypothesis:
H₀ μ₁= μ₂= μ₃
H₁: At least one of the population means is different from the others
Where:
Population 1: line A
Population 2: line B
Population 3: line C
α: 0.01
This test is always one-tailed to the right. The statistic is the Snedecor's F, constructed as the MSTr divided by the MSEr if the value of the statistic is big, this means that there is a greater variance due to the treatments than to the error, this means that the population means are different. If the value of F is small, it means that the differences between populations are not significant ( may differ due to error and not treatment).
The critical region is:
If F ≥ 3.36, the decision is to reject the null hypothesis.
Looking at the given data:
= 11.32653
With this value the decision is to reject the null hypothesis.
Using the p-value method:
p-value: 0.001005
α: 0.01
The p-value is less than the significance level, the decision is to reject the null hypothesis.
At a level of 5%, there is significant evidence to say that at least one of the population means of the production ratio of the assembly lines A, B and C is different than the others.
b) In this item, you have to stop paying attention to the production ratio of the assembly line A to compare the population means of the production ratio of lines B and C.
(I'll use the same subscripts to be congruent with part a.)
The parameter to estimate is μ₂ - μ₃
The populations are the same as before, so you can still assume that the study variables have a normal distribution and their population variances are unknown but equal. The statistic to use under these conditions, since the sample sizes are 6 for both assembly lines, is a pooled-t for two independent variables with unknown but equal population variances.
t= (X[bar]₂ - X[bar]₃) - ( μ₂ - μ₃) ~t
Sa√(1/n₂+1/n₃)
The formula for the interval is:
(X[bar]₂ - X[bar]₃) ± *
Sa= 0.827 ≅ 0.83
X[bar]₂ = 43.33
X[bar]₃ = 41.5
(43.33-41.5) ± 3.169 *
1.83 ± 3.169 * 0.479
[0.31; 3.35]
With a confidence level of 99% you'd expect that the difference of the population means of the production rate of the assemly lines B and C.
I hope it helps!
