Question

Use the following information to answer questions 26 to 29. In October 1998, 30% of employed adults were satisfied with their chances for promotion. A human resource manager wants to determine if this percentage has changed significantly since then. She randomly selects 280 employed adults and find that 112 of them are completely satisfied with their chances for promotion. Is there sufficient evidence to conclude that the percentage of employed adults satisfied with their chances for promotion is significantly different from the percentage in 1998, at the α = 0.1 level of significance?

The null and alternative hypothesis are: A. H0: p = 0.3 versus H1: p ≠ 0.3 B. H0: p = 0.4 versus H1: p ≠ 0.4 C. H0: p = 0.3 versus H1: p < 0.3 D. H0: p = 0.3 versus H1: p > 0.3 5 puntos PREGUNTA

27 The t statistic is equal to: A. z = 1.65 B. z = -1.65 C. t = 3.65 D. t = -3.65

PREGUNTA 28 The critical value is equal to: A. t = ± 3.65 B. z = ± 1.65 C. z = 3.65 D. z = -1.65

PREGUNTA 29 The conclusion is to Reject the Null Hypothesis Verdadero o Falso

Answer 1

Given:

In October 1998, 30% of employed adults were satisfied with their chances for promotion.

n=280

X : completely satisfied with their chances for promotion = 112

p= X/n = 112/280 = 0.4

To test that the there sufficient evidence to conclude that the percentage of employed adults satisfied with their chances for promotion is significantly different from the percentage in 1998.

Ans: A. H0: p = 0.3 versus H1: p ≠ 0.3

test statistic,

C. t statistic = 3.65

α = 0.1

critical value =

B. z = ± 1.65

Here, t statistic = 3.65 > critical value = 1.65

Therefore we Reject Null Hypothesis.

Therefore there is sufficient evidence to conclude that the percentage of employed adults satisfied with their chances for promotion is significantly different from the percentage in 1998 i.e-0.4.