Consider a test of $\mathrm { H } _ { 0 } : \mu = 35$ performed with the computer. SPSS reports a two-tailed p-value of 0.0124. Make the appropriate conclusion for the given situation: $\mathrm { H } _ { \mathrm { a } } : \mu 35 , z = - 2.5 , \alpha = 0.01$
A) Reject $\mathrm { H } _ { 0 }$
B) Fail to reject $\mathrm { H } _ { 0 }$

Question

Consider a test of $\mathrm { H } _ { 0 } : \mu = 35$ performed with the computer. SPSS reports a two-tailed p-value of 0.0124. Make the appropriate conclusion for the given situation: $\mathrm { H } _ { \mathrm { a } } : \mu > 35 , z = - 2.5 , \alpha = 0.01$
A) Reject $\mathrm { H } _ { 0 }$
B) Fail to reject $\mathrm { H } _ { 0 }$

Quizplus · Accepted Answer

The p-value is for a two-tailed test, but the alternative hypothesis suggests a one-tailed test. Since $z = -2.5$ indicates the sample mean is less than the hypothesized mean, and the alternative hypothesis is $\mu > 35$, the direction of the test does not support rejecting $\mathrm { H } _ { 0 }$. Additionally, for a one-tailed test, the p-value should be halved, resulting in 0.0062, which is still less than $\alpha = 0.01$, but the direction of the effect is opposite to the alternative hypothesis. Therefore, we fail to reject $\mathrm { H } _ { 0 }$ based on the direction of the z-score relative to the alternative hypothesis.

Consider a Test Of H0:μ=35\mathrm { H } _ { 0 } : \mu = 35H0​:μ=35

Consider a Test Of $\mathrm { H } _ { 0 } : \mu = 35$