Question

Ava read an article claiming that 10% of people in her county were senior citizens, and she wondered if this held true for residents in her city. She took a random sample of 225 people from her city to test H0 : p = 0.10, where p is the proportion of people in her city that are senior citizens. Ava found that approximately 14% of those sampled were senior citizens. She conducted an appropriate significance test, and the resulting test statistic was z ≈ 1.89z. Assume that the conditions for inference were met.

Answer 1

Complete Question

Ava read an article claiming that 10% of people in her county were senior citizens, and she wondered if this held true for residents in her city. She took a random sample of 225 people from her city to test H0 : p = 0.10, where p is the proportion of people in her city that are senior citizens. Ava found that approximately 14% of those sampled were senior citizens. She conducted an appropriate significance test, and the resulting test statistic was z ≈ 1.89 z. Assume that the conditions for inference were met.calculate the p-value for Ellie's significance test

Answer:

The p-value is  $p-value = 0.0588$

Step-by-step explanation:

From the question we are told that

   The percentage of senior citizens is  p =  0.10  

   The sample size is  $n = 225$

   The  sample proportion is  $\^{p} = 0.14$

   The test statistics is  $z \approx = 1.89$

The null hypothesis  is  $H_o : p = 0.10$

The alternative hypothesis is   $H_a : p \ne 0.10$

   Generally the p-value is mathematically represented as

       $p-value = 2 * P(Z > 1.89 )$

From the z-table  

       $P(Z > 1.89 ) = 0.029379$

=>     $p-value = 2 * 0.029379$

=>     $p-value = 0.0588$