The sign test is performed to test $H _ { 0 } : m = 32 \text { versus } H _ { 1 } : m

Question

The sign test is performed to test $H _ { 0 } : m = 32 \text { versus } H _ { 1 } : m < 32$ . There are 14 positive signs and 19 negative signs in a test involving 33 samples. What is the value of the test statistic?
A) -0.87
B) 0.87
C) 1.04
D) -0.70

Quizplus · Accepted Answer

The sign test statistic formula is given by:
$$z = \frac{n_{+}-n_{-}}{\sqrt{n}}$$
where, 
$n_{+}$ = number of positive signs, 
$n_{-}$ = number of negative signs, 
$n$ = total number of samples.

Substituting the given values in the formula, we get:
$$z = \frac{14-19}{\sqrt{33}} = \frac{-5}{\sqrt{33}} \approx -0.87$$
Therefore, the closest option is D, which is -0.70.

The Sign Test Is Performed to Test H0:m=32 versus H1:m<32H _ { 0 } : m = 32 \text { versus } H _ { 1 } : m < 32H0​:m=32 versus H1​:m<32

The Sign Test Is Performed to Test $H _ { 0 } : m = 32 \text { versus } H _ { 1 } : m < 32$