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Determine the $p$ -value that would be used to test the following hypotheses when $z$ is used as the test statistic. a. $\quad H_{o}: p_{1}=p_{2}$ versus $H_{a}: p_{1}>p_{2},$ with $z *=2.47$b. $\quad H_{o}: p_{A}=p_{B}$ versus, $H_{a}: p_{A} \neq p_{B},$ with $z \star=-1.33$c. $\quad H_{a}: p_{1}-p_{2}=0$ versus $H_{a}: p_{1}-p_{2}<0,$ with $z *=-0.85$d. $\quad H_{o}: p_{m}-p_{f}=0$ versus $H_{a}: p_{m}-p_{f}>0,$ with $z *=3.04$

$$ a. 0.0068\\b. 0.1835\\c. 0.1977\\d. 0.0012$$

Intro Stats / AP Statistics

Chapter 10

Inferences Involving Two Populations

Section 4

Inferences Concerning the Difference between Proportions Using Two Independent Samples

Hypothesis Testing with Two Samples

Temple University

Piedmont College

University of St. Thomas

Boston College

Lectures

03:30

Perform the indicated test…

03:24

Perform the test of hypoth…

04:31

Calculate the test statist…

05:18

01:21

Determine the $p$ -value t…

00:38

Find the P-value for the h…

05:37

Determine the $p$ -value f…

03:12

00:39

00:31

01:09

09:22

00:53

02:46

Compute the value of the t…

Okay, um, in this question, I'm going to use the software are to help us, Um, calculate the Peabody owes. Okay, that's snowcapped heart to pay. The alternative hypothesis is Pete want greater than p two, and our that start is equal to 2.47 So, um, our p value as you go to the probability off they were in them their bows that greater than our, um God, it was that star. Well, I know that this that IHS representing a random bearable which is following Southern normal distribution. And this that star isjust a value board. A number we have, and it is our test statistic. Okay, um, that start with, um are well use function copy, Norm. And how include poor words that star brother. Um, because, um, here, this operator is greater than so We're looking for the right held. So we need Teoh indicate in the function that lower towers, because to fall us here we crack our, um, key value for part A, which is equal to Is there a point they're owed there? Oh, 68 All right, um, and if we draw grabs, who have, like this point to be ours that star 2.47 and our P value here is just the area for this rightto. Okay, let's move to part B part B. The H A as p a does not go to pp can't That star is equal to negative 1.33 So because of this, operators were looking for, um the to tout part. So we're interested in the area both right and left And the summation off. Thesis Blue of Blue Part is our people do. And this Ah, going to be positive. 1.33 And here his hours at Star, which is negative 1.33 Okay, so let's couple live for just 11 part the norms records of 1.33 and we multiply this value by to cause Ping because we just calculated for, um for one site. So our p brother for parts three Azaz there a 0.18 35 Oh, right. We can move to part C part saying we have bought one people on Linus Pete too smaller than their own. And that star is now. Good tip. There a point k five. So we're looking for the probability off that smaller than negative zero point pay. Five. Show pink Norm MCE 2.8 fried and we have our people loot. Which is he? Quote Teoh Arrowpoint 1977 All right, and heart D he l minus p f greater than their own. That star Aziz 3.4 So the P value should be equal to the probability off. Sad, greater than 3.4 Again, that is a random variable which is following the standard normal the distribution. Okay, so it is going to be the right to tell. You're in 3.4 And our P bateau is just the area from 3.4 to the positive infinity. All right, let's calculate this. Number 3.4 lower toe is and we cat P bateau is equal to zero point there. Oh, there are 12

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