Question

Test the claim about the difference between two population means $\mu_1$ and $\mu_2$ at the level of significance $\alpha$. Assume the samples are random and independent, and the populations are normally distributed.\ Claim: $\mu_1 = \mu_2$; $\alpha = 0.10$. Assume $\sigma_1^2 = \sigma_2^2$ Sample statistics: $\bar{x}_1 = 32.8$, $s_1 = 3.6$, $n_1 = 10$ and $\bar{x}_2 = 34.9$, $s_2 = 2.3$, $n_2 = 18$ Identify the null and alternative hypotheses. Choose the correct answer below. A. $H_0: \mu_1 \neq \mu_2$ $H_a: \mu_1 = \mu_2$ C. $H_0: \mu_1 < \mu_2$ $H_a: \mu_1 \geq \mu_2$ E. $H_0: \mu_1 > \mu_2$ $H_a: \mu_1 \leq \mu_2$ Find the standardized test statistic t. t = (Round to two decimal places as needed.) B. $H_0: \mu_1 \leq \mu_2$ $H_a: \mu_1 > \mu_2$ D. $H_0: \mu_1 \geq \mu_2$ $H_a: \mu_1 < \mu_2$ F. $H_0: \mu_1 = \mu_2$ $H_a: \mu_1 \neq \mu_2$

          Test the claim about the difference between two population means $\mu_1$ and $\mu_2$ at the level of significance $\alpha$. Assume the samples are random and independent, and the populations are normally distributed.\
Claim: $\mu_1 = \mu_2$; $\alpha = 0.10$. Assume $\sigma_1^2 = \sigma_2^2$
Sample statistics: $\bar{x}_1 = 32.8$, $s_1 = 3.6$, $n_1 = 10$ and
$\bar{x}_2 = 34.9$, $s_2 = 2.3$, $n_2 = 18$
Identify the null and alternative hypotheses. Choose the correct answer below.
A. $H_0: \mu_1 \neq \mu_2$
$H_a: \mu_1 = \mu_2$
C. $H_0: \mu_1 < \mu_2$
$H_a: \mu_1 \geq \mu_2$
E. $H_0: \mu_1 > \mu_2$
$H_a: \mu_1 \leq \mu_2$
Find the standardized test statistic t.
t = 
(Round to two decimal places as needed.)
B. $H_0: \mu_1 \leq \mu_2$
$H_a: \mu_1 > \mu_2$
D. $H_0: \mu_1 \geq \mu_2$
$H_a: \mu_1 < \mu_2$
F. $H_0: \mu_1 = \mu_2$
$H_a: \mu_1 \neq \mu_2$

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Test the claim about the difference between two population means μ1 and μ2 at the level of significance α. Assume the samples are random and independent, and the populations are normally distributed.Claim: μ1 = μ2; α = 0.10. Assume σ1^2 = σ2^2
Sample statistics: x̅1 = 32.8, s1 = 3.6, n1 = 10 and
x̅2 = 34.9, s2 = 2.3, n2 = 18
Identify the null and alternative hypotheses. Choose the correct answer below.
A. H0: μ1 ≠μ2
Ha: μ1 = μ2
C. H0: μ1 < μ2
Ha: μ1 ≥μ2
E. H0: μ1 > μ2
Ha: μ1 ≤μ2
Find the standardized test statistic t.
t =
(Round to two decimal places as needed.)
B. H0: μ1 ≤μ2
Ha: μ1 > μ2
D. H0: μ1 ≥μ2
Ha: μ1 < μ2
F. H0: μ1 = μ2
Ha: μ1 ≠μ2

Added by Raquel S.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Leanna Arjune

07/28/2022

Step 1

The alternative hypothesis (Ha) is that there is a difference between the two population means, μ1 and μ2. Show more…

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Find the standardized test statistic t Test the claim about the difference between two population means and at the level of significance . Assume the samples are random and independent, and the populations are normally distributed. Claim=;=0.10.Assume= Sample statistics: X, = 32.8, s,=3.6, n, = 10 and X =34.9, s =2.3, n =18 Identify the null and alternative hypotheses. Choose the correct answer below. A.H#2 Ha=2 OC.Ho2 H2 E.H>2 Ha:2 B.H Ha>2 D.Hg2 Ha 2 F.Ho=2 Ha#2 Find the standardized test statistic t. t= (Round to two decimal places as needed.)

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Transcript

00:02 For this question, the biggest thing we need to find here is the p value.

00:05 We're doing a hypothesis test.

00:07 It's going to be a one sample t test.

00:10 And i'll walk you through the steps on finding the hypotheses and our test statistic.

00:16 And then we'll connect that back to the p value.

00:20 So our claim is that our mean, our population mean, is less than 4 ,915, with a significance level of 0 .01.

00:28 Our sample statistics include a sample mean of 5 ,117, our sample standard deviation of 5 ,725, and our sample size of 55.

00:41 And because this is a one sample t test, we're also going to need what's called the degrees of freedom.

00:49 So the degrees of freedom is just going to be in this case, n a minus 1.

00:53 So that's going to be 54.

00:54 And we're going to need that when we're calculating that p value close to the end.

01:01 So now what we need to do is we need to figure out what our hypotheses are.

01:06 So our null hypothesis and our alternative hypothesis, our claim does not have a statement of equality in it.

01:14 So that's going to be our alternative hypothesis.

01:17 So our mean is greater than 4 ,915.

01:21 And our null hypothesis is just going to be the complement.

01:24 So that our mean is greater than or equal to.

01:28 Sorry, our alternative is that it's less than.

01:30 Our mean is less than 4 ,915, and that our null is greater than or equal to 4 ,915.

01:39 Now, based on the sign of the alternative hypothesis, we can determine this is a left tail test.

01:47 So the sign of the alternative hypothesis tells us what kind of test this is going to be.

01:53 And that is also going to be pivotal in our p value...

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