Question

Ellie 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] versus [hₐ:p neq 0.10], where [p] is the proportion of people in her city that are senior citizens. she found that [31] of those sampled were senior citizens, and the corresponding test statistic was [z approx 1.89]. assuming that the necessary conditions are met, what is the approximate p-value for ellie's significance test? you may round to three decimal places.

Answer 1

The approximate p-value for Ellie's significance test is 0.0574.

Step-by-step explanation:

To calculate the approximate p-value for Ellie's significance test, we need to find the area under the standard normal curve that corresponds to the test statistic, which is approximately 1.89. Since this is a two-tailed test, we need to find the area in both tails.

Using a standard normal distribution table or a calculator, we can find that the area to the left of 1.89 is approximately 0.9713. Therefore, the area in both tails is 1 - 0.9713 = 0.0287.

The p-value is twice the area in the tail, so the approximate p-value for Ellie's significance test is 2 * 0.0287 = 0.0574 (rounded to three decimal places).