Calculate the t-test statistic using the standard error from part a. t=At α=0.02 , Use the distribution table to find the critical values for the rejection regiontc=±____ Tests the claim that 41 # p2. Assume the samples are normally distributed, random and independent.of = o}81 = 0.75 ; s2 = 0.74Z1 = 46.83 ; z2 = 47.02n1 = 12 ; n2 = 12Standard ErrorDegrees ofFreedomt-Test Statistic(n1-1) s+ (n2- 1) -(Z1 – 2) – (41 – 42)11t =n2SE1- =ni + n2 – 2n1 + n2 – 2

The null hypothesis is given by, H0 : µ1 = µ2 H1 : µ1 ≠µ2 n1 = 12 , n2 = 12 s1 = 0.75, s2 = 0.74 x1…

Answered: TO Tests the claim that 41 # µ2. Assume…

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

Calculate the t-test statistic using the standard error from part a. t=

At α=0.02 , Use the distribution table to find the critical values for the rejection region
tc=±____

Tests the claim that 41 # p2. Assume the samples are normally distributed, random and independent.
of = o}
81 = 0.75 ; s2 = 0.74
Z1 = 46.83 ; z2 = 47.02
n1 = 12 ; n2 = 12
Standard Error
Degrees of
Freedom
t-Test Statistic
(n1-1) s+ (n2- 1) -
(Z1 – 2) – (41 – 42)
1
1
t =
n2
SE1- =
ni + n2 – 2
n1 + n2 – 2

Expert Solution

Step 1

The null hypothesis is given by,

H₀ : µ₁ = µ₂

H₁ : µ₁ ≠µ₂

n₁ = 12 , n₂ = 12

s₁ = 0.75, s₂ = 0.74

$x_{1} = 46.83, x_{2} = 47.02$

Hence, standard error,

$s_{x_{1} - x_{2}} = \sqrt{\frac{(n_{1} - 1) {s_{1}}^{2} + (n_{2} - 1) {s_{2}}^{2}}{n_{1} + n_{2} - 2}} \cdot \sqrt{\frac{1}{n_{1}} + \frac{1}{n_{2}}} = \sqrt{\frac{11 \times 0 . 75^{2} + 11 \times 0 . 74^{2}}{12 + 12 - 2}} \sqrt{\frac{1}{12} + \frac{1}{12}} = 0.745016778 * 0.40824829 = 0.304151826 \approx 0.3042 (R o u n d e d t o 4 d e c i m a l)$

The test statistic is given by,

$t = \frac{(x_{1} - x_{2}) - (µ_{1} - µ_{2})}{s_{(x_{1} - x_{2})}}$

Under null hypothesis,

$t = \frac{(x_{1} - x_{2}) - 0}{s_{(x_{1} - x_{2})}} = \frac{(x_{1} - x_{2})}{s_{(x_{1} - x_{2})}}$

So, observed value of test statistic , $t = \frac{(x_{1} - x_{2})}{s_{(x_{1} - x_{2})}} = \frac{46.83 - 47.02}{0.304151826} = - 0.624688013 \approx - 0.6247$