Question

Proportion Problem. Each year Delta Dental does a survey of parents concerning the tradition of the Tooth Fairy. A random sample of 1,058 parents were asked about how much money they leave for a tooth and questions concerning how their child responded to the concept of the Tooth Fairy. In one question, 508 parents indicated that their child saved the money they got for their tooth.

You are asked to Test to see if this proportion is different from .5. Use an alpha level of .05.

What is the p-value for your test statistic (z*)? I just want the answer. Use 4 decimal places for your answer and use the proper rules of rounding.

Answer 1

Solution :

This hypothesis test is a two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.50

H_a : p 0.50

= x / n = 508 / 1058 = 0.4802

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.4802 - 0.50 / [(0.50 * 0.50) / 1058]

= -1.291

P-value = 2 *  P(z < -1.291) = 0.1968

P-value = 0.1968