Question

How do professionals stay on top of their​ careers? Of 1,000 surveyed members of a business networking​ website, 510 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 47​%?

State the null and alternative hypotheses.

H0​:π= 0.47

H1​:π≠ 0.47

Calculate the test statistic.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.47

H_a : p 0.47

= x / n = 510 / 1000 = 0.51

P₀ = 0.47

1 - P₀ = 1 - 0.47 = 0.53

Test statistic = z =

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.51 - 0.47/ [(0.47 * 0.53) / 1000 ]

Test statistic = z = 2.53

P(z > 2.53) = 1 - P(z < 2.53) = 1 - 0.9943 = 0.0057

P-value = 0.0114

= 0.05    

P-value <

Reject the null hypothesis.

There is sufficient evidence to suggest that the proportion of all site members who engaged in professional networking within the last month is different from 47​%