Question

in tossing a coin 1024 times we get 460 tails. is this coin fair? use a significance level equal to 5%

Answer 1

in tossing a coin 1024 times we get 460 tails. is this coin fair? use a significance level equal to 5%.

For a fair coin, probability of tail= head=0.5.

Therefore

Ho: P=0.5, H₁: P≠0.5

One sample proportion test used

p=460/1024 =0.4492

= -3.25

Table value of z at 0.05 level = 1.96

Rejection Region: Reject Ho if z < -1.96 or z > 1.96

Calculated z = -3.25 falls in the rejection region

The null hypothesis is rejected.

There is enough evidence to conclude that the coin is not fair.

Z Test of Hypothesis for the Proportion
Data
Null Hypothesis            p =	0.5
Level of Significance	0.05
Number of Items of Interest	460
Sample Size	1024
Intermediate Calculations
Sample Proportion	0.44921875
Standard Error	0.0156
Z Test Statistic	-3.2500
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical Value	1.9600
p-Value	0.0012
Reject the null hypothesis