Answered: Form the hypotheses (null and…

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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Question

Form the hypotheses (null and alternative) and identify the claim

Claim: The average in state tuition is more than $9,410

Ho: µ=9410

H_α: µ>9410

State the distribution and test statistic to be used.

Normal distribution and t-test

Sample mean= 9521

Sample Standard Deviation= 2151

Test statistic= 0.206

p-value= 0.42

Use the previous information to sketch a picture of this situation. CLEARLY, label and scale the horizontal axis and shade the region(s) corresponding to the p-value.

Expert Solution

Step 1

First we find the sample size;

Given that;

$\bar{x} = 9521 s = 2151 t = 0.206 μ = 9410 [U n d e r n u l l h y p o t h e s i s]$

Using the formula of the test statistic we find the value of the sample size.

$t = \frac{\sqrt{n} (\bar{x} - μ)}{s} \Rightarrow 0.206 = \frac{\sqrt{n} (9521 - 9410)}{2151} \Rightarrow \sqrt{n} = \frac{0.206 \times 2151}{(9521 - 9410)} \Rightarrow \sqrt{n} = 3.99 S q u a r i n g b o t h t h e s i d e s w e g e t; \Rightarrow n = 15.92 \Rightarrow n \approx 16$

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