The initial temperature of a cup of tea is 200ºF. The surrounding temperature is 70ºF, and the value of the constant k is 0.6.
1 answer:
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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!
Use this property of logarithms:
Your equation transforms into:
Now, you have to apply the definition of a logarithm to express the equation in exponential form:
In case you don't remember, this is the definition of a logarithm:
The log is the exponent (y) you have to raise the base (b) to in order to get the power (x).
Finally, solve the rational equation:
The correct answer is d.
Your equation transforms into:
Now, you have to apply the definition of a logarithm to express the equation in exponential form:
In case you don't remember, this is the definition of a logarithm:
The log is the exponent (y) you have to raise the base (b) to in order to get the power (x).
Finally, solve the rational equation:
The correct answer is d.