Question

A new cream that advertises that it can reduce wrinkles and improve skin was subject to a recent study. A sample of 40 women over the age of 50 used the new cream for 6 months. Of those 40 women, 30 of them reported skin improvement(as judged by a dermatologist). Is this evidence that the cream will improve the skin of more than 50% of women over the age of 50? Test using α=0.01. (a) Test statistic: z= (b) Critical Value: z=

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.50

H_a : p > 0.50

= x / n = 30 / 40 = 0.75

P₀ = 0.50

1 - P₀ = 0.50

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.75 - 0.50 / [(0.50 * 0.50) / 40]

= 3.16

Test statistic = z = 3.16

   = 0.01

Z_0.01 = 2.326

Critical value = z = 2.326