Discuss the suggestion that the mean height of the universe is 65 inches.

Mumbai University > COMPS > Sem 4 > Applied Mathematics 4

Marks : 06

Year : MAY 2015

N = 10 (< 30, so it is small sample)

Step 1: Null hypothesis $(H_0) : µ = 65$

Alternate hypothesis $(H_0): µ != 65$ [Two tailed test]

Step 2: LOS = 5% (Two tailed test)

Degree of freedom $= n – 1 = 10 – 1 = 9$

Critical value $(t_x) = 2.2622$

Step 3:

$$\overline d=\dfrac {\sum d_i}n=\dfrac 0{10}=0\\ \therefore \overline x=a+\overline d=67+0=67$$

Since sample is small, $s=\sqrt{\dfrac {\sum d_i^2}n-(\sqrt{\dfrac {\sum d_i}n)^2}}\\ =\sqrt{\dfrac {88}{10}-(\dfrac 0{10})^2}\\ =2.9965\\ S.E=\dfrac s{\sqrt{n-1}}=\dfrac {2.9965}{\sqrt 9}=0.9888$

Step 4: Test statistic

$$t_{cal}=\dfrac {\overline x-\mu}{S.E}\\ =\dfrac {67-65}{0.9888}\\ =2.0227$$

Step 5: Decision

Since $|t_{cal}| \lt t_x, H_0$ is accepted.

The man height of the universe is 65 inches.