Question

1. if ( p > alpha ), which conclusion is most appropriate? *

a. reject ( h_0 ); strong evidence for ( h_1 ).
b. fall to reject ( h_0 ); not enough evidence for ( h_1 ).
c. prove that ( h_0 ) is true.
d. change ( alpha ) to make ( p ) smaller.

1. in a quality - control test, a company claims that the average weight of cereal boxes is 500 g. a hypothesis test finds ( p = 0.02 ) at ( alpha = 0.05 ). what conclusion should be made?

a. fall to reject ( h_0 ); there is no significant difference.
b. reject ( h_0 ); the average weight likely differs from 500 g.
c. increase sample size; the result is uncertain.
d. the test proves ( h_1 ) is true.

Explanation:

En un test de hipótesis, la regla es: si \( p < \alpha \), se rechaza \( H_0 \); si \( p > \alpha \), no se rechaza \( H_0 \).

Para la pregunta 7:
Dado que \( p>\alpha \), no se rechaza \( H_0 \), lo que significa que no hay suficiente evidencia para \( H_1 \).

Para la pregunta 8:
Dado que \( p = 0.02<\alpha=0.05 \), se rechaza \( H_0 \), lo que implica que el promedio probablemente difiere de 500 g.

Answer:

1. B. Fall to reject \( H_0 \); not enough evidence for \( H_1 \).
2. B. Reject \( H_0 \); the average weight likely differs from 500 g.