what is the p value

Question

Test the claim that the proportion of people who own cats is significantly different than 30% at the 0.02 significance level. Based on a sample of 800 people, 39% owned cats

The p-value is: Incorrect (to 2 decimals)

Answer 1

Hi Sulekho,

To get the p-value, you first need a test statistic. This problem involves the z-test for one population proportion, which is computed as:

z= (p^- p₀) / sqrt((p₀q₀)/n)

p^= sample proportion = 39% = 0.39

p₀= population proportion under null hypothesis = 30% = 0.30

q_{0 =} 1 - p₀ = 1 - 0.30 = 0.70

n= sample size = 800

A caveat with this formula is you need at least 10 "successes" (people who own cats) and 10 "failures" (people who don't). With n=800, this is not an issue, but you may see problems where it is.

Now, for your test statistic:

z = (0.39 -0.30) / sqrt((0.3*0.7)/800))

z = 5.55

Now, if you look at any z-table, 5.5 most likely will not even appear on it. The probability that Z<5.55 is too close to 1, but remember, you want the two-sided alternative. so you want:

p-value = (1-(P(Z<5.55)))/2

P(Z < 5.55) = 1.00--a virtual lock

p-value = (1 - 1.00)/2

This is essentially 0, so to two decimal places:

p = 0.00

I will leave the conclusion to you. I hope this helps.