Only about 11% of all people can wiggle their ears. Is this % different for millionaires? Of the 303 millionaires surveyed, 18 could wiggle their ears.

Question

What can be concluded at the = 0.10 level of significance? Please just find the test statistic (z), and what p-value is.

Answer 1

Hi Lauren,

For your test statistic, the formula is:

z= (p^-p₀)/sqrt(p₀q₀/n)

p^=sample probability

p₀₌population probability estimate

q₀=1-p₀

n=sample size

So:

p^=18/303= 0.059

p₀=0.11

q₀=0.89

n=303

Substituting:

z= (0.059-0.11)/sqrt(0.11*0.89/303)

z= -2.837

Now, we can go to the z-table for p-value, but remember, this is a two-sided test, so:

look up -2.84--we'll round up--in the z-table:

P(Z<-2.84)= 0.0023

Because this is a two-sided test, we must multiply this value by 2, so:

p= 0.0046

I hope this helps.