Consider the following printout.
HYPOTHESIS: VARIANCE $\mathrm { X } = \mathrm { x }$
$$X = \text { gpa }$$
SAMPLE MEAN OF $X = 2.8731$
SAMPLE VARIANCE OF $X = .18000$
SAMPLE SIZE OF $X = 189$
HYPOTHESIZED VALUE $( x ) = 3.0$
VARIANCE $\mathrm { X } - \mathrm { x } = - .1269$
$$z = - 4.11203$$
State the proper conclusion when testing $H _ { 0 } : \mu = 3.0$ vs. $H _ { \mathrm { a } } : \mu

Question

Consider the following printout.
HYPOTHESIS: VARIANCE $\mathrm { X } = \mathrm { x }$
$$X = \text { gpa }$$
SAMPLE MEAN OF $X = 2.8731$
SAMPLE VARIANCE OF $X = .18000$
SAMPLE SIZE OF $X = 189$
HYPOTHESIZED VALUE $( x ) = 3.0$
VARIANCE $\mathrm { X } - \mathrm { x } = - .1269$
$$z = - 4.11203$$
State the proper conclusion when testing $H _ { 0 } : \mu = 3.0$ vs. $H _ { \mathrm { a } } : \mu < 3.0$ at $\alpha = .05$.
A) Reject $H _ { 0 }$.
B) Accept $\mathrm { H } _ { 0 }$.
C) Fail to reject $H _ { 0 }$.
D) We cannot determine from the information given.

Quizplus · Accepted Answer

Given the z-score of -4.11203 and the hypothesis test $H_0: \mu = 3.0$ vs. $H_a: \mu < 3.0$, a z-score this extreme (far from 0) indicates that the sample mean is significantly lower than the hypothesized mean of 3.0. Since we are testing at the $\alpha = .05$ level and the z-score falls into the critical region (indicating a significant difference), we reject $H_0$.

Consider the Following Printout X=x\mathrm { X } = \mathrm { x }X=x

Consider the Following Printout $\mathrm { X } = \mathrm { x }$