Question

Question 3 Assume that you have a sample of n₁ = 8 from a population with sample mean X₁ = 42 and a sample standard deviation of S₁ = 4, and you have an independent sample of n2 = 15 from another population with sample mean of X₂ = 34 and sample standard deviation S2 = = 5, a) What is the value of the pooled-variance t-test statistic for testing differences in two population means? b) In obtaining the critical value of the test statistic t, how many degrees of freedom are there? c) Using a level of significance of a = 0.01, what is the critical value for one-tail test of the hypothesis Ho: µ₁ <= µ₂ against the alternative H₁: μ > μη? d) What is your statistical decision? e) What assumptions about the two populations must be made? f) Set up a 95% confidence interval estimate of the difference between the population means μ₁ and µ2.

          Question 3
Assume that you have a sample of n₁ = 8 from a population with sample mean X₁ = 42 and a
sample standard deviation of S₁ = 4, and you have an independent sample of n2 = 15 from
another population with sample mean of X₂ = 34 and sample standard deviation S2 = = 5,
a) What is the value of the pooled-variance t-test statistic for testing differences in two
population means?
b) In obtaining the critical value of the test statistic t, how many degrees of freedom are
there?
c) Using a level of significance of a = 0.01, what is the critical value for one-tail test of
the hypothesis Ho: µ₁ <= µ₂ against the alternative H₁: μ > μη?
d) What is your statistical decision?
e) What assumptions about the two populations must be made?
f) Set up a 95% confidence interval estimate of the difference between the population
means μ₁ and µ2.

Show more…

question 3 assume that you have a sample of n1 8 from a population with sample mean x1 42 and a sample standard deviation of s1 4 and you have an independent sample of n2 15 from another pop 55293

Added by Belen F.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert David Nguyen

08/05/2022

Step 1

Step 1: The pooled-variance t-test statistic is calculated as: $$t = \frac{\bar{X_1} - \bar{X_2}}{s_p \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}$$ where: * $\bar{X_1}$ is the sample mean of the first population * $\bar{X_2}$ is the sample mean of the second Show more…

Show all steps

lock

Thanks for your feedback!

Question 3 Assume that you have a sample of n₁ = 8 from a population with sample mean X₁ = 42 and a sample standard deviation of S₁ = 4, and you have an independent sample of n2 = 15 from another population with sample mean of X₂ = 34 and sample standard deviation S2 = = 5, a) What is the value of the pooled-variance t-test statistic for testing differences in two population means? b) In obtaining the critical value of the test statistic t, how many degrees of freedom are there? c) Using a level of significance of a = 0.01, what is the critical value for one-tail test of the hypothesis Ho: µ₁ <= µ₂ against the alternative H₁: μ > μη? d) What is your statistical decision? e) What assumptions about the two populations must be made? f) Set up a 95% confidence interval estimate of the difference between the population means μ₁ and µ2.

Play audio

Feedback

Powered by NumerAI

David Nguyen and 89 other subject Intro Stats / AP Statistics educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

00:01 Hi, i'm david and i'm here to have you and sing your questions.

00:03 Here we have several questions and let me answer one by one for you.

00:07 Let me pick it up.

00:09 Let me make it bigger.

00:12 This will be the first two questions and let me go back and take another one.

00:19 Here we will have the second one.

00:22 It will be, we want to have from the 2046 up to this one and then i put it down here.

00:49 Let me make it bigger and then we have the last pair this one will be question 47 ready and then we have the question 48 and i will put the question 48 down here make it bigger okay now let me go back in the first question now from this one we have the hyper test testing and we need to compute the test statistics now the test statistics here t is equal to the x -par minus the mean over the s devang square to the n so x -par here it will get equal to the 20 .76 the mean equal to the 20 over the s it will equal to the 12 divided by square into the 36 and if we compute we have the 0 .76 the 1 b12 times 6 equal to the 0 .38 therefore, the answer will be the option a here.

02:08 Now let's move to the question next one here.

02:13 It will be the following sample data from the normal.

02:17 One is the point estimate and the proportion mean.

02:20 So from here we'll find to find the mean x bar.

02:23 It'll just go to the sum and everything divided by n.

02:26 Therefore let me pass the data into the calculator.

02:29 2, 4, 3, 2, 4.

02:34 And then we will have the sum equal to the 15 divided by the n equal to the 5 and equal to the 3.

02:44 Now found the answer will be the option a here.

02:48 And we have the same dataset as in the previous question...

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later