Write the equation of the line y = 3x + 5 when dilated by a scale factor of 2 centered
1 answer:
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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
Answer:
Step-by-step explanation:
1) 4x -3
x = -7 ;
4x - 3 = 4*(-7) - 3 = - 28 - 3 = -31
x = 14 ;
4x - 3 = 4*14 - 3 = 56 - 3 = 53
x = 0
4x - 3 = 0 - 3 = -3
2) 6 -3x
x = -7 ;
6 - 3x = 6 - 3*(-7) = 6 + 21 = 27
x = 14
6 - 3x = 6 - 3*14 = 6 - 42 = -36
x = 0
6 - 3x = 6 - 0 = 6
4)
