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

P-value ≈ 0.0588

Explanation:

Answer 2

The value is
`z = 3`

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) =  (k)/(n)`

=>
`\^(p) =  (  36 )/(225)`

=>
`\^(p) =0.16`

Generally the test statistics is mathematically represented as

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

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

=>
`z = 3`