A set of 5 coins is tossed 3200 times and the number of heads appearing each time is noted. The results are given below: No. of Heads 0 1 2 3 4 5
Frequency 80 570 1100 900 500 50
Test the hypothesis that the coins are unbiased
Answers
Answer:
the hypothesis that the coins are unbiased is rejected
Step-by-step explanation:
Let say coins are unbiased
then probability of head = Probability of Tail = 1/2
Chances of no head = ⁵C₀(1/2)⁰(1/2)⁵ = 1/32 => (1/32)*3200 = 100
Chances of 1 Head = ⁵C₁(1/2)¹(1/2)⁴ = 5/32 => (5/32)*3200 = 500
Chances of 2 Head = ⁵C₂(1/2)²(1/2)³ = 10/32 => (5/32)*3200 = 1000
Chances of 3 Head = ⁵C₃(1/2)³(1/2)² = 10/32 => (5/32)*3200 = 1000
Chances of 4 Head = ⁵C₄(1/2)⁴(1/2)¹ = 5/32 => (5/32)*3200 = 500
Chances of 5 head = ⁵C₅(1/2)⁵(1/2)⁰ = 1/32 => (1/32)*3200 = 100
Occurance Event Probability ( O-E)² (O-E)²/E
80 100 400 4
570 500 4900 9.8
1100 1000 10000 10
900 1000 10000 10
500 500 0 0
50 100 2500 25
Sum of (O-E)²/E = 58.8
Value is higher than the expected
Null hypothesis is rejected
Answer:
Step-by-step explanation: