Question

Fair coin? You want to determine if a coin is fair. So you toss it $10$times and record the proportion of tosses that land “heads.” You would like to perform a test of $H_0:p=0.5$versus $H_a:p\ne 0.5$, where $p$= the proportion of all tosses of the

coin that would land “heads.” Check if the conditions for performing the significance test are met.

Short answer

No, all the conditions are not satisfied.

Step-by-step solution

Given Information

It is given that $n=10$

$p=0.50$

The null and alternate hypothesis are:

$H_0:p=0.50$

$H_a:p\ne 0.50$

$p$are the proportion of coins that land head.

Calculations

The conditions to fulfilled for significance test are:

• $n\times p\ge 10$: role="math" localid="1654610961025" $n\times p=10\times 0.5=5<10$
  
• $n\times (1-p)\ge 10$: $n\times (1-p)=10\times (1-0.5)=5<10$
  

Both conditions are not fulfilled. Hence, significance test cannot be performed.