Question

A suggestion is made that the proportion of people who have food allergies and/or sensitivities is 0.66. You believe that the proportion is actually less than 0.66. The hypotheses for this test are Null Hypothesis: p ≥ 0.66, Alternative Hypothesis: p < 0.66. If you select a random sample of 20 people and 13 have a food allergy and/or sensitivity, what is your test statistic and p-value?

Answer 1

Answer)

Null hypothesis Ho : P >= 0.66

Alternate hypothesis Ha : P < 0.66

N = 20

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 13.2

N*(1-p) = 6.8

Both the conditions are met so we can use standard normal z table to estimate the P-Value

Test statistics z = (oberved p - claimed p)/standard error

Standard error = √{claimed p*(1-claimed p)/√n

Observed P = 13/20

Claimed P = 0.66

N = 20

After substution

Test statistics Z = -0.09

From z table, P(z<-0.09) = 0.4641

So, P-value = 0.4641