Question

Ten individuals are chosen at random from a population and heights are
found to be 63,63,64,65,66,69,69,70,70,71 inches. Discuss the suggestion that
the height of universe is 65 inches.
​

Answer 1

Given:

xi = 63, 63, 64, 65, 66, 69, 69, 70, 70, 71

n = 10

μ = 65 inches

To find:

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

Solution:

∑xi = 63 + 63 + 64 + 65 + 66 + 69 + 69 + 70 + 70 + 71 = 670

x = ∑xi / n = 670/10 = 67

xi          Di = (xi - x)          Di²  

63              -4                   16

63              -4                   16

64              -3                    9

65              -2                    4

66              -1                     1

69               2                    4

69               2                    4

70               3                    9  

70               3                    9

71                4                   16

                                 ∑Di = 88

$S = \sqrt{\frac{\sum D_i^{2} }{n-1} }\\\\S = \sqrt{\frac{88}{10 - 1} }\\\\S = \sqrt{\frac{88}{9} }$

S = 3.1269

The null hypothesis H₀: μ = 65 inches

The alternative hypothesis: μ ≠ 65 inches

Critical value (tₓ) = 2.2622

The df = n - 1 = 10 - 1 = 9

$t = \frac{|x - \mu |}{S}\sqrt{n}\\\\t = \frac{|67 - 65|}{3.1269}\sqrt{10}$

t = 2.0226

Since |t| < tₓ, H₀ is accepted

Therefore, the height of the universe is 65 inches.