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Answer:
We conclude that there is an equal or larger proportion of Republicans in favor of lowering the standards.
Step-by-step explanation:
<u>The complete question is</u>: A nationwide sample of influential Republicans and Democrats was asked as a part of a comprehensive survey whether they favored lowering environmental standards so that high-sulfur coal could be burned in coal-fired power plants. The results were:
Number sampled: 1,000 (republican) , 800 (democrats)
Number in favor: 200 (republican) , 168 (democrats)
At the 0.02 level of significance, can we conclude that there is a larger proportion of Democrats in favor of lowering the standards? Determine the p-value.
Let = <u><em>proportion of Republicans in favor of lowering the standards</em></u>.
= <u><em>proportion of Democrats in favor of lowering the standards</em></u>.
SO, Null Hypothesis, :
{means that there is an equal or larger proportion of Republicans in favor of lowering the standards}
Alternate Hypothesis, :
{means that there is a larger proportion of Democrats in favor of lowering the standards}
The test statistics that would be used here <u>Two-sample z-test for</u> <u>proportions</u>;
T.S. = ~ N(0,1)
where, = sample proportion of Republicans in favor of lowering the standards =
= 0.20
= sample proportion of Democrats in favor of lowering the standards =
= 0.21
= sample of Republicans = 1000
= sample of Democrats = 800
So, <u><em>the test statistics</em></u> =
= -0.52
The value of z test statistics is -0.52.
<u>Now, P-value of the test statistics is given by the following formula; </u>
P-value = P(Z < -0.52) = 1 - P(Z 0.52)
= 1 - 0.6985 = 0.3015
Now, at 0.02 significance level, the z table gives a critical value of -2.054 for left-tailed test.
Since our test statistic is more than the critical value of z as -0.52 > -2.054, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <em><u>we fail to reject our null hypothesis</u></em>.
Therefore, we conclude that there is an equal or larger proportion of Republicans in favor of lowering the standards.
Answer:
J. The equation has one real solution and two complex solutions.
Step-by-step explanation:
Complex solutions come in pairs, so there can only be an even number of them. So we can rule out G, H, and K.
To find the other roots, we can factor using either long division or grouping. To use long division, see the attached picture. To use grouping:
3x³ − 4x² + x − 10 = 0
3x³ − 6x² + 2x² + x − 10 = 0
3x² (x − 2) + (2x + 5) (x − 2) = 0
(x − 2) (3x² + 2x + 5) = 0
The other factor is 3x² + 2x + 5. The discriminant of this is (2)² − 4(3)(5) = -56. Since the discriminant is negative, the roots are complex.
