Question

As businesses rush to cash in on the popularity of the World Wide Web (WWW), questions have arisen as to what WWW services users would be willing to pay for. A research institute surveyed 13,000 randomly selected WWW users and asked them about their willingness to pay fees for access to web sites. Of these, 2,938 were definitely NOT willing to pay such fees.

The research institute wishes to test if the proportion of WWW users who will not pay such fees is less than 25%. The researcher tests the following hypotheses:

H0: p = 0.25

HA: p ≠0.25

What is the p-value for the test?

Select the correct answer below:

• 2.6358

• -6.3195

• 0.0000

• 0.226

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.25

H_a : p 0.25

= x / n = 2938 / 13000 = 0.2260

P₀ = 0.25

1 - P₀ = 0.75

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.226 - 0.25 / [(0.25 * 0.75) / 13000]

= -6.32

P(z < -6.32) = 0

P-value = 2 * 0 = 0.0000