Answer to Question #226060 in Statistics and Probability for Carrie

Question

The following table contains information on matched sample values upon which the differences

calculated between the two samples are assumed to be normally distributed.

Number 1 2 3 4 5 6 7 8

Sample 1 18 12 21 22 16 14 17 18

Sample 2 21 11 23 20 20 17 17 22

The E–Tutor wants to test whether the mean difference differ from zero.

Which one of the following statements is incorrect?

1. The hypothesis are: H0 : D D 0 vs H1 : D 6D 0:

2. The sample mean is .

Answer 1

Statement 1

$H_o: \mu_0=0\\ H_1: \mu_0=0\\$

Statement 2

$\bar{d}= \frac{\sum d_i}{n}= -1.625$

$s.d = \sqrt{\frac{\sum d_i^2-(d_i)^2}{n-1}}= 2.3261$

Statement 3

$s_e= \frac{s_d}{\sqrt{n}}= \frac{2.3261}{\sqrt{8}}=0.8224$

Statement 4

$t= \frac{\bar{d}}{s_e}= \frac{-1.625}{0.8224}=-1.9759$

Statement 5

Reject if t < -t₇

t< -3.499

Hence the fifth statement is false