Which fraction is equivalent
2 answers:
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Answer:
Step-by-step explanation:
Hello!
The objective is to test if rising the process temperature reduces the thickness of the plastic film that coats a substrate material To do so, two samples of substrates are coated at different temperatures:
Sample 1
X₁: Thickness of the plastic film after the substrate is coated at 125F
n₁=11
X[bar]₁= 101.28
S₁= 5.08
Sample 2
X₂: Thickness of the plastic film after the substrate is coated at 150F
n₂= 13
X[bar]₂= 101.70
S₂= 20.15
Does the data support this claim? Use the P-value approach and assume that the two population standard deviations are not equal.
Now if the higher the heat, the thinner the thickness of the plastic coating, then the average thickness of the coating done at 150F should be less than the average thickness of the coating done at 125F, symbolically: μ₂ < μ₁
Then the hypotheses are:
H₀: μ₂ ≥ μ₁
H₁: μ₂ < μ₁
α:0.05 (there is no α level stated so I've chosen the most common one)
Assuming that both variables have a normal distribution since the population standard deviations are not equal, the statistic to use is the Welch's t-test:
This test is one-tailed to the left, meaning that you'll reject the null hypothesis at small values of t. The p-value is also one-tailed and has the same direction as the test. To calculate it you have to first calculate the degrees of freedom of the Welch's t:
The distribution is a Student's t with 13 degrees of freedom, then you can calculate the p-value as:
P(t₁₃≤0.072)= 0.4718
Using the p-value approach, the decision rule is:
If the p-value ≤ α, the decision is to reject the null hypothesis.
If the p-value > α, the decision is to not reject the null hypothesis.
The p-value is greater than the significance level, so the decision is to nor reject the null hypothesis.
Using a significance level of 5%, there is no significant evidence to support the claim that the average thickness pf the plastic coat processed at 150F is less than the average thickness pf the plastic coat processed at 125F.
I hope you have a SUPER day!
Answer:
D. a = 60 and b = 58.8
Step-by-step explanation:
Z-score:
In a set with mean and standard deviation
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Z-score for data point a is 0.
This means that a is the mean, that is, a = 60.
The z-score for data point b is -0.4.
This means that b must be a value below the mean, that is, a value below 60.
The option that satisfies a = 60 and b < 60 is option D, which is the answer.