Math question: solve for x. -7.8(x + 6.5) = -25.74
1 answer:
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Answer:
Step-by-step explanation:
The slope of a graph is also known as its gradient, which is the steepness of the graph.
If we are given two points on the line, we can find the slope by taking rise/ run, which is the ratio of the change in y-coordinate against the change in the x-coordinate. This can also be written as a formula:
☆ (x₁, y₁) is the first coordinate and (x₂, y₂) is the second coordinate
In this question, we are given the equation of the line. This equation is already in the slope-intercept form (y= mx +c) since the coefficient of y is 1 and all the other terms are on the other side of the equal sign. In the slope-intercept form, m is the slope while c is the y-intercept.
m= ⅘ since the coefficient of x is ⅘ in the given equation (when the equation is in the slope-intercept form).
Answer:
a. two-tailed test
b. reject H0 if Z>1.96 or Z<-1.96
c. Z = 1.73
d. we have failed to reject the null hypothesis
e. P-value = 0.0418
Step-by-step explanation:
We will use a Z test to resolve this, an it will be a two-tailed test because the hypothesis statements are not indicating a specific direction for the significant difference (H0 : μ1 = μ2 ; H1 : μ1 ≠ μ2), this also means that the significanclevel will be divided between the both tails (2.5% en each tail for the rejection regions). See attached drawing for reference.
We need to find our critical value:
Zα/2 = Z(0.05/2) = 0.025
If we look for 0.025 in a Z table we will find that the critical value is 1.96 to the right, and by symmetry -1.96 to the left. So our decision rule will be to reject H0 if Z>1.96 or Z<-1.96
The Z test will be done using the next equation:
Z = (x⁻1 - x⁻2) - (μ1 - μ2) / √( σ²1/n1 + σ²2/n2
Because we are testing the null hypothesis we know that μ1 - μ2 must be zero if they are supposed to be equal (H0 : μ1 = μ2), so we calculate as follows:
Z = (100.5 - 98.8) - (0) / √( (3.4)²/38 + (5.8)²/51 = 1.7/0.9817 = 1.73
Z<1.96, therefore we have failed to reject the null hypothesis
The P-value for this test would be represented by the probability of Z being greater than 1.73, so we can look for it in any Z table, finding that its value is 0.0418, and because P-value>0.025 we again confirm that we don't have evidence statistically significant to reject the null hypothesis
