Question

Apply t-test to the following data sets and compare it with the value of u=4. Identify the test and find the critical value and state the conclusion
a) 2 3 4 5 6 7 b) 1 2 2 5 5 7

Answer 1

Answer:

a)0.654

b)-0.34

Step-by-step explanation:

a)2 3 4 5 6 7

$\mu = 4$

$Mean = \frac{\text{Sum of all observations}}{\text{No. of observations}}\\Mean = \frac{2+3+4+5+6+7}{6}\\Mean =4.5$

Standard deviation $=\sqrt{\frac{\sum(x-\bar{x})^2}{n-1}}$

Standard deviation $=\sqrt{\frac{(2-4.5)^2+(3-4.5)^2+(4-4.5)^2+(5-4.5)^2+(6-4.5)^2+(7-4.5)^2}{6-1}}=1.87$

$t=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}\\t=\frac{4.5-4}{\frac{1.87}{\sqrt{6}}}\\t=0.654$

Df = n-1 = 6-1 = 5

Assume α=0.05

So$t_{(\alpha,df)}=t_{0.05,5}=2.57$

So, t critical = 2.57

So, t calculated < t critical

b)1 2 2 5 5 7

$\mu = 4 \\Mean = \frac{\text{Sum of all observations}}{\text{No. of observations}}\\Mean = \frac{1+2+2+5+5+7}{6}\\Mean =3.67$

Standard deviation =$\sqrt{\frac{\sum(x-\bar{x})^2}{n-1}}$

Standard deviation =$\sqrt{\frac{(1-3.67)^2+(2-3.67)^2+(2-3.67)^2+(5-3.67)^2+(5-3.67)^2+(7-3.67)^2}{6-1}}=2.338$

$t=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}t=\frac{3.67-4}{\frac{2.338}{\sqrt{6}}}t=-0.34$

Df = n-1 = 6-1 = 5

Assume α=0.05

So, $t_{(\alpha,df)}=t_{0.05,5}=2.57$

So, t critical = 2.57

So, t calculated < t critical