Question

Ellie read an article claiming that 10% of people in her county were senior citizens, and she thought that it may be higher for residents in her city. She took a random sample of 225 people from her city and found that 36 of them were senior citizens. She wants to test H0:p=0.10 versus Ha:p > 0.10, where p is the proportion of people in her city that are senior citizens. Assuming that the conditions for inference have been met.
Required:
Calculate the test statistic for Ellie's significance test.

Answer 1

Answer:

The  value is $z = 3$

Step-by-step explanation:

From the question we are told that

   The  population proportion of senior citizens is  $p = 0.10$

   The  sample size is  $n = 225$

   The  number of senior citizens is  k =  36

   The  null hypothesis is  $H_o : p = 0.10$

    The alternative hypothesis is  $H_a : p > 0.10$

Generally the sample proportion is mathematically represented as

     $\^{p} = \frac{k}{n}$

=>   $\^{p} = \frac{ 36 }{225}$

=>  $\^{p} =0.16$

Generally the test statistics is mathematically represented as

     $z = \frac{\^{p} - p }{\sqrt{\frac{p(1 -p )}{n} } }$

=>    $z = \frac{0.16 - 0.10 }{\sqrt{\frac{p(1 -0.10)}{225} } }$

=>    $z = 3$