Answer:
(a) The data indicate a significant difference between the two treatments.
(b) The data do not indicate a significant difference between the two treatments.
(c) The data indicate a significant difference between the two treatments.
Step-by-step explanation:
Null hypothesis: There is no difference between the two treatments.
Alternate hypothesis: There is a significant difference between the two treatments.
Data given:
M1 = 55
M2 = 52
s1^2 = 8
s2^2 = 4
n1 = 12
n2 = 12
Pooled variance = [(n1-1)s1^2 + (n2-1)s2^2] ÷ (n1+n2-2) = [(12-1)8 + (12-1)4] ÷ (12+12-2) = 132 ÷ 22 = 6
Test statistic (t) = (M1 - M2) ÷ sqrt [pooled variance (1/n1 + 1/n2)] = (55 - 52) ÷ sqrt[6(1/6 + 1/6)] = 3 ÷ 1.414 = 2.122
Degree of freedom = n1+n2-2 = 12+12-2 = 22
(a) For a two-tailed test with a 0.05 (5%) significance level and 23 degrees of freedom, the critical values are -2.069 and 2.069.
Conclusion:
Reject the null hypothesis because the test statistic 2.122 falls outside the region bounded by the critical values.
(b) For a two-tailed test with a 0.01 (1%) significance level and 23 degrees of freedom, the critical values are -2.807 and 2.807.
Conclusion:
Fail to reject the null hypothesis because the test statistic 2.122 falls within the region bounded by the critical values.
(c) For a one-tailed test with 0.05 (5%) significance level and 23 degrees of freedom, the critical value is 1.714.
Conclusion:
Reject the null hypothesis because the test statistic 2.122 is greater than the critical value 1.714.
13) As they’ve given the zeros, you can use those to create factors. Since the zeros are x=-1, x=-3, and x=4, by making the right side 0 in each equation, you get the factors (x+1), (x+3), and (x-4). Then, you can multiply those factors using box method or FOIL or whichever method you prefer. By multiplying (x+1) and (x+3), I got x^2+4x+3. Then, I multiplied that by (x-4) to get x^3-13x-12, which is your final answer.
14) Using the same steps in 13, I found the factors. As the zeros are x=-6 and x=0, I got the factors (x) and (x+6). Then, I multiplied them and got x^2+6x, which is the answer.
15) x=1, x=1, x=2. These become the factors (x-1), (x-1), and (x-2). Then, by multiplying (x-1) and (x-1) you get x^2-2x+1. Multiply that by (x-2) to get your final answer, x^3-4x^2+5x-2.
16) Zeros are x=-1, x=5, and x=-2. You get the factors (x+1), (x-5), and (x+2). Multiply (x+1) and (x-5) to get x^2-4x-5. Multiply that by the other factor, (x+2), to get your final answer, x^3-2x^2-13x-10.
Equation D does not give the correct value of w because P= 2W + 2L. If needed I can explain more in depth.
