You wish to test the following claim (HaHa) at a significance level of α=0.001α=0.001. Ho:p1=p2Ho:p1=p2 Ha:p1≠p2Ha:p1≠p2 You obtain 186 successes in a sample of size n1=286n1=286 from the first population. You obtain 264 successes in a sample of size n2=486n2=486 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution. What is the critical value for this test? (Report answer accurate to three decimal places.) critical value = ±± What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = The test statistic is... in the critical region not in the critical region This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the first population proportion is not equal to the second population proprtion. There is not sufficient evidence to warrant rejection of the claim that the first population proportion is not equal to the second population proprtion. The sample data support the claim that the first population proportion is not equal to the second population proprtion. There is not sufficient sample evidence to support the claim that the first population proportion is not equal to the second population proprtion.

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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You wish to test the following claim (HaHa) at a significance level of α=0.001α=0.001.

Ho:p1=p2Ho:p1=p2
Ha:p1≠p2Ha:p1≠p2

You obtain 186 successes in a sample of size n1=286n1=286 from the first population. You obtain 264 successes in a sample of size n2=486n2=486 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.

What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value = ±±

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

The test statistic is...

in the critical region
not in the critical region

This test statistic leads to a decision to...

reject the null
accept the null
fail to reject the null

As such, the final conclusion is that...

There is sufficient evidence to warrant rejection of the claim that the first population proportion is not equal to the second population proprtion.
There is not sufficient evidence to warrant rejection of the claim that the first population proportion is not equal to the second population proprtion.
The sample data support the claim that the first population proportion is not equal to the second population proprtion.
There is not sufficient sample evidence to support the claim that the first population proportion is not equal to the second population proprtion.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution

Step 1

Hey, since there are multiple subparts posted, we will answer first three subparts. If you want any specific subpart to be answered then please submit that subpart only or specify the subpart in your message.

The critical value for this test is calculated as below:

The critical value is obtained from Excel using function "=NORMSINV(probability)

Output obtained from Excel is given below:

From the outputs, the critical value is $\pm 3.291$

Thus, the critical value= $\pm 3.291$

Step 2

The value of ${\hat{p}}_{1}$ is obtained below:

$\begin{array}{rcl} {\hat{p}}_{1} & = & \frac{186}{286} \\ = & 0.6503 \end{array}$

The value of ${\hat{p}}_{2}$ is obtained below:

$\begin{array}{rcl} {\hat{p}}_{2} & = & \frac{264}{486} \\ = & 0.5432 \end{array}$

The pooled value $\hat{p}$ is obtained below:

$\begin{array}{rcl} \hat{p} & = & \frac{186 + 264}{286 + 486} \\ = & \frac{450}{772} \\ = & 0.5829 \end{array}$

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