Question

An article predicts that "spit," spam that is delivered via internet phone lines and cell phones, will be a growing problem as more people turn to web-based phone services. In a poll of 5500 cell phone users, 15% indicated that they had received commercial messages and ads on their cell phones. Is there sufficient evidence that the proportion of cell phone users who have received commercial messages or ads in 2004 was greater than the proportion of 0.13 reported for the previous year? (Use α = 0.05. Round your test statistic to two decimal places and your P-value to four decimal places.)

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.13

H_a : p > 0.13

n = 5500

= 0.15

P₀ = 0.13

1 - P₀ = 0.87

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.15 - 0.13 / [(0.13 * 0.87) / 5500]

= 4.41

P(z > 4.41) = 1 - P(z < 4.41) = 1 - 1 = 0

P-value = 0