Question

How do professionals stay on top of their​ careers? Of 1 comma 000 surveyed members of a business networking​ website, 450 reported that they engaged in professional networking within the last month. At the 0.05 level of​ significance, is there evidence that the proportion of all site members who engaged in professional networking within the last month is different from 42​%?

a. state the full hypothesis

b. calculate the test statistic.

Zstat=

c. what is the P value?

Answer 1

a)

H0: p = 0.42

Ha: p 0.42

b)

Sample proportion = 450 / 1000 = 0.45

Zstat = - p / sqrt( p (1 - p) / n)

= 0.45 - 0.42 / sqrt( 0.42 * 0.58 / 1000)

= 1.92

c)

p-value for two tailed test is

p-value = 2 * P( Z > z)

= 2 * P( Z > 1.92)

= 2 * 0.0274 (Probability calculated from Z table)

= 0.0548

Since p-value > 0.05 significance level, do not reject the null hypothesis.