What was the main environmental goal of New Deal projects such as the Civilian Conservation Corps and the Works Progress Adminis
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Answer and Step-by-step explanation: Scaterplot is a type of graphic which shows the relationship between to variables. In this question, you want to determine if there is a linear relationship between overhead widths of seals and the weights. So, the hypothesis are:
H₀: no linear correlation;
H₁: there is linear correlation;
In this hypothesis test, to reject H₀, the correlation coefficient r of the data set has to be bigger than the critical value from the table.
With α = 0.05 and n = 6, the critical value is 0.811.
The linear correlation is calculated as:
r = n∑xy - ∑x.∑y / √[n∑x² - (∑x)²] [n∑y² - (∑y)²]
r =
r = 0.9485
Since r is bigger than the critical value, H₀ is rejected, which means there is enough evidence to conclude that there is linear correlation between overhead widths and the weights.
In the attachments is the scaterplot of the measurements, also showing the relationship.
Answer:
(a) The distribution of (Y - X) is <em>N</em> (0.001, 0.0005).
(b) The probability that the pin will not fit inside the collar is 0.023.
Step-by-step explanation:
The random variable <em>X</em> is defined as the diameter of the pin and the random variable <em>Y</em> is defined as the diameter of the collar.
The distribution of <em>X</em> and <em>Y</em> is:
The random variables <em>X</em> and <em>Y</em> are independent of each other.
(a)
Compute the expected value of (Y - X) as follows:
The mean of (Y - X) is 0.001.
Compute the variance of (Y - X) as follows:
The standard deviation of (Y - X) is 0.0005.
Thus, the distribution of (Y - X) is <em>N</em> (0.001, 0.0005).
(b)
Compute the probability of [(Y - X) ≤ 0] as follows:
*Use a <em>z</em>-table for the probability value.
Thus, the probability that the pin will not fit inside the collar is 0.023.