Please answer B, C, & D. Only 20% of registered voters voted in the last election. Will voter participation decline for the upcomingelection? Of the 388 randomly selected registered voters surveyed, 58 of them will vote in the upcomingelection. What can be concluded at the a = 0.01 level of significance?a. For this study, we should use z-test for a population proportion vb. The null and alternative hypotheses would be:Ho: ?v Select an answer v(please enter a decimal)Hj: ?v| Select an answer v(Please enter a decimal)c. The test statistic ?v =(please show your answer to 3 decimal places.)d. The p-value(Please show your answer to 4 decimal places.)e. The p-value isaf. Based on this, we should rejectthe null hypothesis.g. Thus, the final conclusion is that ...O The data suggest the population proportion is not significantly lower than 20% at a = 0.01, sothere is statistically significant evidence to conclude that the percentage of registered voterswho will vote in the upcoming election will be equal to 20%.%3DO The data suggest the population proportion is not significantly lower than 20% at a = 0.01, sothere is statistically insignificant evidence to conclude that the percentage of registered voterswho will vote in the upcoming election will be lower than 20%.%3DThe data suggest the populaton proportion is significantly lower than 20% at = 0.01, so thereis statistically significant evidence to conclude that the the percentage of all registered voterswho will vote in the upcoming election will be lower than 20%.%3D

b. The null and alternate hypotheses are as below: H0:p0=0.2H1:p0<0.2 c. Here p^=58388=0.1495…

Answered: Only 20% of registered voters voted in…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Please answer B, C, & D.

Only 20% of registered voters voted in the last election. Will voter participation decline for the upcoming
election? Of the 388 randomly selected registered voters surveyed, 58 of them will vote in the upcoming
election. What can be concluded at the a = 0.01 level of significance?
a. For this study, we should use z-test for a population proportion v
b. The null and alternative hypotheses would be:
Ho: ?v Select an answer v
(please enter a decimal)
Hj: ?v| Select an answer v
(Please enter a decimal)
c. The test statistic ?v =
(please show your answer to 3 decimal places.)
d. The p-value
(Please show your answer to 4 decimal places.)
e. The p-value is
a
f. Based on this, we should reject
the null hypothesis.
g. Thus, the final conclusion is that ...
O The data suggest the population proportion is not significantly lower than 20% at a = 0.01, so
there is statistically significant evidence to conclude that the percentage of registered voters
who will vote in the upcoming election will be equal to 20%.
%3D
O The data suggest the population proportion is not significantly lower than 20% at a = 0.01, so
there is statistically insignificant evidence to conclude that the percentage of registered voters
who will vote in the upcoming election will be lower than 20%.
%3D
The data suggest the populaton proportion is significantly lower than 20% at = 0.01, so there
is statistically significant evidence to conclude that the the percentage of all registered voters
who will vote in the upcoming election will be lower than 20%.
%3D

Expert Solution

Step 1

The null and alternate hypotheses are as below:

$H_{0} : p_{0} = 0.2 H_{1} : p_{0} < 0.2$

Here

$\begin{array}{rcl} \hat{p} & = & \frac{58}{388} \\ = & 0.1495 \end{array}$

The test statistic is obtained as follows:

$\begin{array}{rcl} z & = & \frac{\hat{p} - p_{0}}{\sqrt{\frac{p_{0} (1 - p_{0})}{n}}} \\ = & \frac{0.1495 - 0.2}{\sqrt{\frac{0.2 (0.8)}{388}}} \\ = & \frac{- 0.0505}{0.0203} \\ = & - 2.4868 \end{array}$

Thus, the test statistic is -2.4868

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