Alice wants to fence in a rectangular pay area for her rabbits. The length of the area should be at least 20ft, and the distance
1 answer:
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Answer:
The probability that a defective rod can be salvaged = 0.50
Step-by-step explanation:
Given that:
A machine shop produces heavy duty high endurance 20-inch rods
On occasion, the machine malfunctions and produces a groove or a chisel cut mark somewhere on the rod.
If such defective rods can be cut so that there is at least 15 consecutive inches without a groove.
Then; The defective rod can be salvaged if the groove lies on the rod between 0 and 5 inches i.e ( 20 - 15 )inches
Now:
P(X ≤ 5) =
= 0.25
P(X ≥ 15) =
= 0.25
The probability that a defective rod can be salvaged = P(X ≤ 5) + P(X ≥ 15)
= 0.25+0.25
= 0.50
∴ The probability that a defective rod can be salvaged = 0.50
Answer:
(C) The slope of the regression equation is not significantly different from zero
Step-by-step explanation:
Let's suppose that we have the following linear model:
Where Y is the dependent variable and X the independent variable. represent the intercept and
the slope.
In order to estimate the coefficients we can use least squares estimation.
If we are interested in analyze if we have a significant relationship between the dependent and the independent variable we can use the following system of hypothesis:
Null Hypothesis:
Alternative hypothesis:
Or in other wouds we want to check is our slope is significant.
In order to conduct this test we are assuming the following conditions:
a) We have linear relationship between Y and X
b) We have the same probability distribution for the variable Y with the same deviation for each value of the independent variable
c) We assume that the Y values are independent and the distribution of Y is normal
The significance level is provided and on this case is
The standard error for the slope is given by this formula:
Th degrees of freedom for a linear regression is given by since we need to estimate the value for the slope and the intercept.
In order to test the hypothesis the statistic is given by:
The confidence interval for the slope would be given by this formula:
And using the last formula we got that the confidence interval for the slope coefficient is given by:
IF we analyze the confidence interval contains the value 0. So we can conclude that we don't have a significant effect of the slope on this case at 5% of significance. And the best option would be:
(C) The slope of the regression equation is not significantly different from zero