Two-way table correct countincorrect countrow total Version A40575480 Version B47248520 Inferential statistics n1n2 phat 1phat 2 480520 0.843750.907692308 Estimate of the difference between population proportions phat1-phat2 -0.06394231 standard error of estimate 0.020788831 Confidence interval you are 95% confident that p1-p2 is between -0.10468842 and -0.0231962 0 is NOT in the confidence interval so there is strong evidence there is a diffference in proportions hypothesis testing test stat two sided pvalue -3.07580107 0.002099379 To calculate the p-value H0: p1=p2 is assumed to be true since the test is two-sided H1 is H1: p1≠p2 Calculate the z test stat for sample proportion,Use wolframalpha.com to find “probability Z distribution> z test stat” using the answers in part (1) for example if find the test stat is -0.5 enterprobability Z distribution > -0.5Into wolfram alpha3.Comment on the confidence interval for p1- p24. Comment on the Pvalue for testing the claim p1- p2=0

Answered: ble correct count…

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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Related questions

Question

	Two-way table
	correct count	incorrect count	row total
Version A	405	75	480
Version B	472	48	520

Inferential statistics
n1	n2		phat 1	phat 2
480	520		0.84375	0.907692308
Estimate of the difference between population proportions
phat1-phat2
-0.06394231
standard error of estimate
0.020788831
Confidence interval
you are 95% confident that p1-p2 is between
-0.10468842
and
-0.0231962
0 is NOT in the confidence interval so there is strong evidence there is a diffference in proportions

hypothesis testing
test stat		two sided pvalue
-3.07580107		0.002099379
To calculate the p-value H0: p1=p2 is assumed to be true
since the test is two-sided H1 is H1: p1≠p2

Calculate the z test stat for sample proportion,
Use wolframalpha.com to find “probability Z distribution> z test stat” using the answers in part (1) for example if find the test stat is -0.5 enter

probability Z distribution > -0.5

Into wolfram alpha

3.Comment on the confidence interval for p₁- p₂

4. Comment on the Pvalue for testing the claim p₁- p₂=0

Statistics that allow for inferences or estimates about the population. Inferential statistics enable analysts come to conclusions about the population based on sample data. Inferential statistics cover the basics of inferential statistics, all kinds of hypotheses tests and their confidence intervals, design of experiments, and statistical power and errors. It also includes point estimation techniques, limit theorems, sampling distributions, approximations, and bounds. Correlation, regression, and association are also covered under inferential statistics to infer relationships between variables.

Expert Solution

Step 1

The hypothesis testing for difference between proportions of two populations

1	$p_{1}$	$σ_{p_{1}}$
2	$p_{2}$	$σ_{p_{2}}$

Null Hypothesis: There is no difference between two population proportions is stated as:

$H_{0} : p_{1} - p_{2} = 0$

Alternate Hypothesis : $H_{1} : p_{1} - p_{2} \neq 0$

$z = \frac{(\bar{p_{1}} - \bar{p_{2}})}{σ_{(\bar{p_{1}} - \bar{p_{2}})}}; σ_{(\bar{p_{1}} - \bar{p_{2}})} = \sqrt{\frac{p_{1} (1 - p_{1})}{n_{1}} + \frac{p_{2} (1 - p_{2})}{n_{2}}}$